Gr 12 Mathematics: Ch 9 Sum Probability
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Questions and Answers

What is the probability of the union of two mutually exclusive events A and B?

  • P(A) + P(B) (correct)
  • P(A) / P(B)
  • P(A) - P(B)
  • P(A) × P(B)

What is the complementary rule in probability?

  • P(not A) = P(A) + 1
  • P(not A) = 1 - P(A) (correct)
  • P(not A) = P(A)
  • P(not A) = P(A) - 1

What is the purpose of a Venn diagram in probability?

  • To show the probability of an event
  • To visualize the relationships between events (correct)
  • To simplify complex probability problems
  • To calculate the probability of an event

What is the product rule for independent events?

<p>P(A and B) = P(A) × P(B) (A)</p> Signup and view all the answers

What is the definition of mutually exclusive events?

<p>Events that cannot occur simultaneously (C)</p> Signup and view all the answers

What is the symbol for the sample space in probability?

<p>S (A)</p> Signup and view all the answers

What is the purpose of a tree diagram in probability?

<p>To organize and visualize the different possible outcomes of a sequence of events (D)</p> Signup and view all the answers

What is the definition of complementary events?

<p>Events that are mutually exclusive and make up the whole sample space (B)</p> Signup and view all the answers

What is the formula for the probability of the intersection of two events A and B?

<p>P(A) × P(B) (A)</p> Signup and view all the answers

What is the purpose of a two-way contingency table in probability?

<p>To organize and record the counts or percentages in a probability problem (C)</p> Signup and view all the answers

What is the addition rule for any two events A and B?

<p>P(A or B) = P(A) + P(B) - P(A and B) (C)</p> Signup and view all the answers

What is the simplification of the addition rule for two mutually exclusive events?

<p>P(A or B) = P(A) + P(B) (C)</p> Signup and view all the answers

What is the complementary rule?

<p>P(not A) = 1 - P(A) (D)</p> Signup and view all the answers

What is the product rule for independent events?

<p>P(A and B) = P(A) × P(B) (B)</p> Signup and view all the answers

What is the condition for two events to be mutually exclusive?

<p>P(A and B) = 0 (C)</p> Signup and view all the answers

What is the condition for two events to be independent?

<p>P(A and B) = P(A) × P(B) (A)</p> Signup and view all the answers

Why is it incorrect to assume that mutually exclusive events are independent?

<p>Because mutually exclusive events do not satisfy the product rule. (B)</p> Signup and view all the answers

What should you verify to test whether events are independent?

<p>P(A and B) = P(A) × P(B) (A)</p> Signup and view all the answers

What is the formula for the probability of two independent events A and B occurring?

<p>P(A) × P(B) (B)</p> Signup and view all the answers

What is the formula for the total number of outcomes in two events A and B, where there are n(A) outcomes in event A and n(B) outcomes in event B?

<p>n(A) × n(B) (D)</p> Signup and view all the answers

What is the definition of A' in probability theory?

<p>The complement of set A (C)</p> Signup and view all the answers

What is the formula for the total number of arrangements of n different objects?

<p>n! (D)</p> Signup and view all the answers

What is the definition of n! (read as 'n factorial')?

<p>The product of all positive integers up to n (C)</p> Signup and view all the answers

What is the formula for calculating the probability of an event A not occurring?

<p>1 - P(A) (A)</p> Signup and view all the answers

What is the formula for the total number of outcomes when there are n objects to choose from and you choose from them r times?

<p>n^r (B)</p> Signup and view all the answers

What is the formula for the probability of two mutually exclusive events A and B occurring?

<p>P(A) + P(B) (A)</p> Signup and view all the answers

What is the value of 0! (zero factorial)?

<p>1 (B)</p> Signup and view all the answers

What is the purpose of the Fundamental Counting Principle?

<p>To count the number of outcomes in multiple events (B)</p> Signup and view all the answers

What is the value of 0!?"

<p>1 (D)</p> Signup and view all the answers

What is the number of ways to arrange 5 different objects?

<p>120 (D)</p> Signup and view all the answers

If 8 athletes participate in a 400 m race, how many ways can the first three places be arranged?

<p>336 (C)</p> Signup and view all the answers

What is the formula to find the total number of arrangements of 7 distinct objects?

<p>7! (C)</p> Signup and view all the answers

How many arrangements are possible for the letters in the word 'BASSOON'?

<p>2520 (A)</p> Signup and view all the answers

What is the probability of an event when there are 10 favorable outcomes and 100 total outcomes?

<p>1/10 (C)</p> Signup and view all the answers

What is the number of possible PINs if each of the four digits can be any of the 10 digits (0-9)?

<p>10000 (B)</p> Signup and view all the answers

What is the formula to find the total number of arrangements of n distinct objects?

<p>n! (A)</p> Signup and view all the answers

What is the property of factorial notation that states the factorial of any non-negative integer n is the product of all positive integers less than or equal to n?

<p>Property 1 (B)</p> Signup and view all the answers

If the constraint in an arrangement problem is that the youngest and oldest must sit together, how do you treat this pair?

<p>as a single entity (B)</p> Signup and view all the answers

What is the total number of possible PINs if digits cannot be repeated?

<p>5,040 (B)</p> Signup and view all the answers

What is the probability of a PIN containing at least one 8 if digits can be repeated?

<p>0.3439 (C)</p> Signup and view all the answers

What is the number of possible number plates consisting of 3 letters followed by 3 digits?

<p>926,100 (A)</p> Signup and view all the answers

What is the probability that the number plate starts with 'Y' and ends with an odd digit?

<p>0.216 (C)</p> Signup and view all the answers

What is the total number of possible arrangements of the word 'BASSOON' if repeated letters are treated as identical?

<p>1,260 (C)</p> Signup and view all the answers

What is the number of arrangements of the word 'BASSOON' starting and ending with the same letter?

<p>120 (C)</p> Signup and view all the answers

What is the probability that the word 'BASSOON' starts and ends with the same letter?

<p>0.0952 (C)</p> Signup and view all the answers

What is the total number of possible PINs if digits can be repeated?

<p>10,000 (D)</p> Signup and view all the answers

What is the purpose of the addition rule in probability?

<p>To find the probability of the union of two events (C)</p> Signup and view all the answers

What is the condition for two events to be independent?

<p>P(A and B) = P(A) × P(B) (B)</p> Signup and view all the answers

What is the formula for the probability of the complement of an event A?

<p>1 - P(A) (B)</p> Signup and view all the answers

What is true about mutually exclusive events?

<p>P(A and B) = 0 (D)</p> Signup and view all the answers

What is the difference between mutually exclusive and independent events?

<p>Mutually exclusive means P(A and B) = 0, while independent means P(A and B) = P(A) × P(B) (C)</p> Signup and view all the answers

When can the addition rule be simplified to P(A or B) = P(A) + P(B)?

<p>When A and B are mutually exclusive (B)</p> Signup and view all the answers

What is the formula for the probability of the intersection of two independent events A and B?

<p>P(A and B) = P(A) × P(B) (D)</p> Signup and view all the answers

What is the relationship between the probability of an event and its complement?

<p>P(A) + P(A') = 1 (B)</p> Signup and view all the answers

What is the condition for two events to be mutually exclusive?

<p>The events must not have any common outcomes. (A)</p> Signup and view all the answers

What is the formula for the probability of the union of two mutually exclusive events A and B?

<p>P(A) + P(B) (B)</p> Signup and view all the answers

What is represented by the region outside the shape in a Venn diagram?

<p>The outcomes not in the event (C)</p> Signup and view all the answers

What is the probability of an event A not occurring, given P(A) = 0.6?

<p>0.4 (C)</p> Signup and view all the answers

What is the purpose of a two-way contingency table?

<p>To show the relationship between two events (C)</p> Signup and view all the answers

What is the symbol for the sample space?

<p>S (B)</p> Signup and view all the answers

What is the formula for the probability of two independent events A and B occurring?

<p>P(A) × P(B) (A)</p> Signup and view all the answers

What is the condition for two events to be complementary?

<p>The events must be mutually exclusive and make up the whole sample space. (B)</p> Signup and view all the answers

What is the purpose of a tree diagram?

<p>To organize and visualize the different possible outcomes of a sequence of events (A)</p> Signup and view all the answers

What is the probability of event A, given P(not A) = 0.3?

<p>0.7 (C)</p> Signup and view all the answers

What is the formula for the probability of event A not occurring?

<p>1 - P(A) (D)</p> Signup and view all the answers

What is the total number of outcomes when there are n objects to choose from and you choose from them r times, with repetition allowed?

<p>n × n × ... (r times) (C)</p> Signup and view all the answers

What is the formula for the total number of arrangements of n different objects?

<p>n × (n - 1) × ... × 1 (B), n! (D)</p> Signup and view all the answers

What is the purpose of the fundamental counting principle?

<p>To count the number of outcomes in multiple events (B)</p> Signup and view all the answers

What is the condition for two events to be independent?

<p>The occurrence of one event does not affect the probability of the other event (A)</p> Signup and view all the answers

What is the formula for the probability of two independent events A and B occurring?

<p>P(A) × P(B) (B)</p> Signup and view all the answers

What is the formula for the total number of outcomes in two events A and B, where there are n(A) outcomes in event A and n(B) outcomes in event B?

<p>n(A) × n(B) (B)</p> Signup and view all the answers

What is the definition of n! (read as 'n factorial')?

<p>The product of all positive integers up to n (A)</p> Signup and view all the answers

What is the total number of possible arrangements of 7 distinct objects?

<p>7 × 6 × 5 × 4 × 3 × 2 × 1 (A), 7! (B)</p> Signup and view all the answers

What is the value of 0! (zero factorial)?

<p>1 (B)</p> Signup and view all the answers

What is the total number of possible arrangements of 5 different objects?

<p>5! (B), 5 × 4 × 3 × 2 × 1 (C)</p> Signup and view all the answers

What is the total number of ways to arrange the first three places in a 400 m race with 8 athletes?

<p>336 (A), 8 × 7 × 6 (D)</p> Signup and view all the answers

What is the total number of arrangements of the letters in the word 'BASSOON'?

<p>7! / (2! × 2!) (A)</p> Signup and view all the answers

What is the probability of an event when there are 20 favourable outcomes and 100 total outcomes?

<p>20/100 (D)</p> Signup and view all the answers

What is the total number of possible PINs if each of the four digits can be any of the 10 digits (0-9)?

<p>10^4 (A), 10 × 10 × 10 × 10 (B), 10,000 (D)</p> Signup and view all the answers

What is the property of factorial notation that states the factorial of any non-negative integer n is the product of all positive integers less than or equal to n?

<p>n! = the product of all positive integers less than or equal to n (A)</p> Signup and view all the answers

If the constraint in an arrangement problem is that the youngest and oldest must sit together, how do you treat this pair?

<p>As a single entity (B)</p> Signup and view all the answers

What is the total number of arrangements of the letters in the word 'BASSOON' if repeated letters are treated as identical?

<p>7! / (2! × 2!) (A)</p> Signup and view all the answers

What is the probability of an event when there are 10 favourable outcomes and 50 total outcomes?

<p>10/50 (C)</p> Signup and view all the answers

What is the formula for the probability of an event E?

<p>P(E) = n(E) / n(S) (B)</p> Signup and view all the answers

If a PIN consists of 4 digits (0-9) with no repetition, what is the total number of possible PINs?

<p>5040 (D)</p> Signup and view all the answers

What is the probability of a PIN containing at least one 8 if digits can be repeated?

<p>0.3439 (A)</p> Signup and view all the answers

If a number plate consists of 3 letters (excluding vowels and 'Q') followed by 3 digits (0-9), what is the total number of possible number plates?

<p>926100 (B)</p> Signup and view all the answers

What is the probability that the number plate starts with 'Y' and ends with an odd digit?

<p>0.216 (C)</p> Signup and view all the answers

For the word 'BASSOON', what is the total number of possible arrangements if repeated letters are treated as identical?

<p>1260 (D)</p> Signup and view all the answers

What is the probability that the word 'BASSOON' starts and ends with the same letter?

<p>0.0952 (B)</p> Signup and view all the answers

If a PIN consists of 4 digits (0-9) with repetition, what is the total number of possible PINs?

<p>10000 (C)</p> Signup and view all the answers

What is the number of PINs with no 8's if digits can be repeated?

<p>6561 (C)</p> Signup and view all the answers

If P(A) = 0.3 and P(B) = 0.5, what is P(A or B) if A and B are independent?

<p>0.65 (C)</p> Signup and view all the answers

If P(A and B) = 0.2 and P(A) = 0.4, what is P(B) if A and B are independent?

<p>0.5 (D)</p> Signup and view all the answers

What is P(not A) if P(A) = 0.7?

<p>0.3 (C)</p> Signup and view all the answers

If P(A) = 0.2 and P(B) = 0.6, what is P(A and B) if A and B are mutually exclusive?

<p>0 (C)</p> Signup and view all the answers

What is the relationship between P(A) and P(not A)?

<p>P(A) + P(not A) = 1 (C)</p> Signup and view all the answers

If P(A or B) = 0.8 and P(A and B) = 0.2, what is P(A)?

<p>0.6 (C)</p> Signup and view all the answers

What is true about mutually exclusive and independent events?

<p>Mutual exclusivity and independence are distinct concepts (B)</p> Signup and view all the answers

If P(A) = 0.5 and P(B) = 0.3, what is P(A or B) if A and B are dependent?

<p>Cannot be determined (A)</p> Signup and view all the answers

What is the condition for two events to be mutually exclusive?

<p>P(A and B) = 0 (C)</p> Signup and view all the answers

What is the purpose of a two-way contingency table?

<p>To keep a record of the counts or percentages in a probability problem (D)</p> Signup and view all the answers

What is the formula for the probability of the complement of an event A?

<p>P(A') = 1 - P(A) (B)</p> Signup and view all the answers

What is the symbol for the sample space in probability?

<p>S (B)</p> Signup and view all the answers

What is true about complementary events?

<p>They are mutually exclusive and make up the whole sample space (C)</p> Signup and view all the answers

What is the purpose of a Venn diagram in probability?

<p>To visualize the relationship between events (A)</p> Signup and view all the answers

What is the formula for the probability of two independent events A and B occurring?

<p>P(A and B) = P(A) × P(B) (B)</p> Signup and view all the answers

What is the condition for two events to be independent?

<p>P(A and B) = P(A) × P(B) (A)</p> Signup and view all the answers

What is the formula for the union of two events A and B?

<p>P(A ∪ B) = P(A) + P(B) - P(A ∩ B) (A)</p> Signup and view all the answers

What is the purpose of the product rule in probability?

<p>To calculate the probability of the intersection of two events (C)</p> Signup and view all the answers

What is the probability of a PIN containing at least one 8 if digits cannot be repeated?

<p>0.4 (A)</p> Signup and view all the answers

What is the total number of possible number plates consisting of 3 letters followed by 3 digits?

<p>926,100 (C)</p> Signup and view all the answers

What is the number of arrangements of the word 'BASSOON' starting and ending with the same letter?

<p>120 (C)</p> Signup and view all the answers

What is the probability that a PIN contains at least one 8 if digits can be repeated?

<p>0.3439 (C)</p> Signup and view all the answers

If two events A and B are independent, which of the following is true?

<p>P(A ∩ B) = P(A) × P(B) (C)</p> Signup and view all the answers

What is the total number of possible PINs if digits cannot be repeated?

<p>5,040 (C)</p> Signup and view all the answers

If A and B are two events such that A ⊆ B, then which of the following is true?

<p>P(A) ≤ P(B) (A)</p> Signup and view all the answers

What is the probability that the number plate starts with 'Y' and ends with an odd digit?

<p>0.216 (C)</p> Signup and view all the answers

If there are 5 different objects, how many ways are there to arrange them?

<p>5! (D)</p> Signup and view all the answers

What is the total number of possible arrangements of the word 'BASSOON' if repeated letters are treated as identical?

<p>1,260 (D)</p> Signup and view all the answers

What is the probability that the word 'BASSOON' starts and ends with the same letter?

<p>0.0952 (A)</p> Signup and view all the answers

If A and B are two mutually exclusive events, then which of the following is true?

<p>P(A ∩ B) = 0 (A)</p> Signup and view all the answers

If there are 10 objects to choose from and you choose from them 3 times, how many possible outcomes are there?

<p>10^3 (A)</p> Signup and view all the answers

If A is an event, what is the probability of not A?

<p>P(A') = 1 - P(A) (D)</p> Signup and view all the answers

If there are 5 different objects, how many ways are there to arrange 3 of them?

<p>5 × 4 × 3 (D)</p> Signup and view all the answers

What is the formula for the probability of the union of two events A and B?

<p>P(A ∪ B) = P(A) + P(B) - P(A ∩ B) (B)</p> Signup and view all the answers

What is the value of 0!?

<p>1 (C)</p> Signup and view all the answers

If there are 5 different objects, how many ways are there to arrange them in a circle?

<p>(5 - 1)! (B)</p> Signup and view all the answers

What is the total number of ways to arrange the letters in the word 'BASSOON' if the repeated letters are treated as identical?

<p>630 (D)</p> Signup and view all the answers

If seven boys are sitting in a row, and the youngest and oldest must not sit together, what is the total number of arrangements?

<p>3600 (D)</p> Signup and view all the answers

What is the total number of ways to arrange the first three places in a 400m race with 8 athletes?

<p>336 (C)</p> Signup and view all the answers

What is the formula to find the total number of arrangements of n distinct objects?

<p>$n imes (n - 1) imes (n - 2) imes \cdots imes 3 imes 2 imes 1$ (B)</p> Signup and view all the answers

What is the probability of a random arrangement of letters starting and ending with a specific letter?

<p>1/8 (A)</p> Signup and view all the answers

If the constraint in an arrangement problem is that the youngest and oldest must sit together, how do you treat this pair?

<p>As one entity (B)</p> Signup and view all the answers

What is the total number of possible PINs if each of the four digits can be any of the 10 digits (0-9)?

<p>10000 (C)</p> Signup and view all the answers

What is the formula to find the probability of an event E?

<p>$P(E) = rac{n(E)}{n(S)}$ (D)</p> Signup and view all the answers

What is the property of factorial notation that states the factorial of any non-negative integer n is the product of all positive integers less than or equal to n?

<p>The first property of factorial notation (B)</p> Signup and view all the answers

What is the total number of ways to arrange the letters in the word 'BASSOON' if repeated letters are treated as different?

<p>5040 (C)</p> Signup and view all the answers

If two events A and B are independent, what is the value of P(A and B) - P(A)P(B)?

<p>0 (A)</p> Signup and view all the answers

What is the probability of the union of two events A and B, given that P(A) = 0.4, P(B) = 0.3, and P(A and B) = 0.2?

<p>0.7 (A)</p> Signup and view all the answers

If P(A) = 0.6 and P(not A) = 0.4, what is the value of P(A or not A)?

<p>1 (C)</p> Signup and view all the answers

What is the probability of the intersection of two events A and B, given that P(A) = 0.5, P(B) = 0.7, and they are independent?

<p>0.35 (C)</p> Signup and view all the answers

If two events A and B are mutually exclusive, what is the value of P(A and B)?

<p>0 (A)</p> Signup and view all the answers

What is the purpose of the complementary rule in probability?

<p>To find the probability of the complement of an event (D)</p> Signup and view all the answers

If two events A and B are independent, what is the value of P(A) - P(A and B)?

<p>0 (D)</p> Signup and view all the answers

What is the relationship between mutually exclusive and independent events?

<p>Mutually exclusive and independent are distinct concepts (D)</p> Signup and view all the answers

Which of the following is true about mutually exclusive events?

<p>They never occur simultaneously and have an empty intersection. (A)</p> Signup and view all the answers

What is the purpose of a tree diagram in probability?

<p>To organize and visualize the different possible outcomes of a sequence of events. (C)</p> Signup and view all the answers

If two events A and B are dependent, then:

<p>P(A and B) ≠ P(A) × P(B). (C)</p> Signup and view all the answers

What is the formula for the probability of the complement of an event A?

<p>P(not A) = 1 - P(A). (A)</p> Signup and view all the answers

What is the purpose of a two-way contingency table in probability?

<p>To keep a record of the counts or percentages in a probability problem. (D)</p> Signup and view all the answers

What is the symbol for the sample space in probability?

<p>S. (B)</p> Signup and view all the answers

What is the formula for the probability of two independent events A and B occurring?

<p>P(A and B) = P(A) × P(B). (B)</p> Signup and view all the answers

What is the condition for two events to be mutually exclusive?

<p>P(A and B) = 0. (D)</p> Signup and view all the answers

What is the purpose of Venn diagrams in probability?

<p>To show how events are related to one another. (C)</p> Signup and view all the answers

What is true about the intersection of two mutually exclusive events?

<p>It is always empty. (D)</p> Signup and view all the answers

If A and B are two events such that P(A) = 0.3 and P(B) = 0.4, and P(A and B) = 0.12, then what is P(A or B)?

<p>0.64 (B)</p> Signup and view all the answers

If A and B are two independent events such that P(A) = 0.25 and P(B) = 0.5, then what is P(A and B)?

<p>0.125 (B)</p> Signup and view all the answers

If a box contains 5 red balls, 3 blue balls, and 2 green balls, and a ball is drawn at random, what is the probability that it is not blue?

<p>7/10 (A)</p> Signup and view all the answers

If 5 digits are chosen from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} with repetition allowed, what is the total number of possible outcomes?

<p>10^5 (D)</p> Signup and view all the answers

If 3 letters are chosen from the set {A, B, C, D, E, F} without repetition, what is the total number of possible outcomes?

<p>6P3 (A)</p> Signup and view all the answers

If A and B are two events such that P(A) = 0.6 and P(B) = 0.4, and P(A or B) = 0.8, then what is P(A and B)?

<p>0.2 (C)</p> Signup and view all the answers

If a fair six-sided die is rolled 4 times, what is the total number of possible outcomes?

<p>6^4 (C)</p> Signup and view all the answers

If 7 different books are arranged on a shelf, what is the total number of possible arrangements?

<p>7! (D)</p> Signup and view all the answers

If A and B are two independent events such that P(A) = 0.4 and P(B) = 0.3, then what is P(not A and not B)?

<p>0.58 (C)</p> Signup and view all the answers

If a committee of 4 people is chosen from a group of 10 people, what is the total number of possible committees?

<p>10C4 (B)</p> Signup and view all the answers

If the digits in a PIN cannot be repeated, what is the probability that the PIN contains at least one 8?

<p>0.4 (B)</p> Signup and view all the answers

What is the total number of possible number plates consisting of 3 letters (excluding vowels and 'Q') followed by 3 digits (0-9)?

<p>926,100 (C)</p> Signup and view all the answers

For the word 'BASSOON', what is the probability that the word starts and ends with the same letter?

<p>0.0952 (C)</p> Signup and view all the answers

What is the total number of possible PINs if each of the four digits can be any of the 10 digits (0-9)?

<p>10,000 (C)</p> Signup and view all the answers

If the digits in a PIN can be repeated, what is the probability that the PIN contains at least one 8?

<p>0.3439 (A)</p> Signup and view all the answers

What is the probability that a number plate starts with 'Y' and ends with an odd digit?

<p>0.216 (C)</p> Signup and view all the answers

For the word 'BASSOON', what is the total number of possible arrangements if repeated letters are treated as identical?

<p>1,260 (B)</p> Signup and view all the answers

If the digits in a PIN cannot be repeated, what is the total number of possible PINs?

<p>5,040 (C)</p> Signup and view all the answers

How many ways can the letters in the word 'STATISTIC' be arranged?

<p>10! / (2! × 2! × 1! × 1!) (B)</p> Signup and view all the answers

What is the total number of possible arrangements of 9 distinct objects?

<p>9! (C)</p> Signup and view all the answers

A password consists of 6 characters, where each character can be any of the 26 lowercase English letters. How many possible passwords are there?

<p>26^6 (A)</p> Signup and view all the answers

What is the total number of possible arrangements of 5 distinct objects, where one object is fixed in one position?

<p>4! (C)</p> Signup and view all the answers

What is the total number of possible arrangements of the letters in the word 'MISSISSIPPI'?

<p>11! / (4! × 4! × 2!) (B)</p> Signup and view all the answers

How many ways can 8 athletes be arranged in a 400 m race?

<p>8! (A)</p> Signup and view all the answers

What is the total number of possible arrangements of the letters in the word 'BANANA'?

<p>6! / (3! × 2!) (A)</p> Signup and view all the answers

What is the total number of possible arrangements of the letters in the word 'ORANGE'?

<p>6! / (2! × 1!) (A)</p> Signup and view all the answers

What is the total number of possible arrangements of 7 distinct objects, where the youngest and oldest objects must sit together?

<p>6! × 2! (B)</p> Signup and view all the answers

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