Gr12 Mathematics: Ch 9.1 Identities

What is the formula for the probability of an event and its complement?

$P(A) + P(A') = 1$ (correct)

$P(A) imes P(A') = 1$

$P(A) - P(A') = 1$

$P(A) + P(A') = 0$

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

$P(A \cap B) = 1$

$P(A \cap B) = 0$ (correct)

$P(A \cup B) = 1$

$P(A \cup B) = 0$

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

$P(A \cup B) = P(A) / P(B)$

$P(A \cup B) = P(A) + P(B)$ (correct)

$P(A \cup B) = P(A) - P(B)$

$P(A \cup B) = P(A) imes P(B)$

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

$P(A) + P(B) - P(A ext{ and } B)$ Signup and view all the answers

What does the symbol $A'$ represent in probability?

The complement of event A Signup and view all the answers

What is the formula for the probability of two independent events?

$P(A \cap B) = P(A) imes P(B)$ Signup and view all the answers

What is the condition for the addition rule to simplify to $P(A ext{ or } B) = P(A) + P(B)$?

Events A and B are mutually exclusive Signup and view all the answers

What is the sample space represented by in probability?

$S$ Signup and view all the answers

What is the formula for the complementary rule?

$P( ext{not } A) = 1 - P(A)$ Signup and view all the answers

What is the condition for two events to be dependent?

$P(A \cap B) eq P(A) imes P(B)$ Signup and view all the answers

What is the condition for two events A and B to be independent?

$P(A ext{ and } B) = P(A) imes P(B)$ Signup and view all the answers

What is the relationship between mutual exclusivity and independence?

Mutual exclusivity and independence are distinct concepts Signup and view all the answers

What is the term for events that are mutually exclusive and make up the whole sample space?

Complementary events Signup and view all the answers

What is the purpose of the product rule?

To find the probability of the intersection of two independent events Signup and view all the answers

What is the difference between the addition rule and the product rule?

The addition rule is for the union of two events, while the product rule is for the intersection of two events Signup and view all the answers

Why is it important to verify if $P(A ext{ and } B) = P(A) imes P(B)$ when testing for independence?

To ensure that the events are independent Signup and view all the answers

What is the relationship between the probabilities of two events and their union and intersection as expressed by the addition rule?

The probability of the union is the sum of the probabilities of the events minus the probability of their intersection. Signup and view all the answers

What is the condition for the addition rule to simplify to P(A or B) = P(A) + P(B)?

Events A and B are mutually exclusive. Signup and view all the answers

What is represented by P(not A)?

The probability of the complement of event A. Signup and view all the answers

When are two events A and B independent?

When P(A and B) = P(A) × P(B). Signup and view all the answers

What can be concluded about two events A and B if P(A and B) = 0?

They are mutually exclusive. Signup and view all the answers

What is necessary to verify when testing whether two events are independent?

P(A and B) = P(A) × P(B). Signup and view all the answers

What can be said about the relationship between the probabilities of two mutually exclusive events?

The probability of their union is the sum of their probabilities. Signup and view all the answers

What is the purpose of the complementary rule?

To find the probability of an event and its complement. Signup and view all the answers

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

P(A) + P(B) Signup and view all the answers

If two events A and B are independent, what is the probability of A and B not occurring?

1 - P(A) × P(B) Signup and view all the answers

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

P(A') = 1 - P(A) Signup and view all the answers

What is the term for the set of all possible outcomes in a probability experiment?

Sample space Signup and view all the answers

If A is an event, what is the notation for the number of elements in set A?

n(A) Signup and view all the answers

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

P(A ∩ B) = P(A) × P(B) Signup and view all the answers

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

P(A) + P(A') = 1 Signup and view all the answers

If two events A and B are mutually exclusive, what is the probability of their intersection?

P(A ∩ B) = 0 Signup and view all the answers

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

P(A) + P(B) Signup and view all the answers

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

No condition is necessary Signup and view all the answers

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

0.15 Signup and view all the answers

If A and B are dependent, what can be said about P(A and B)?

P(A and B) ≠ P(A)P(B) Signup and view all the answers

What is P(not A) in terms of P(A)?

1 - P(A) Signup and view all the answers

If P(A or B) = 0.7 and P(A) = 0.4, what is P(B) if A and B are mutually exclusive?

0.3 Signup and view all the answers

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

P(A) + P(not A) = 1 Signup and view all the answers

If A and B are independent, what is P(A and not B) in terms of P(A) and P(B)?

P(A)(1 - P(B)) Signup and view all the answers

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

P(A and B) = P(A) × P(B) Signup and view all the answers

What is the probability of the union of two events A and B, if they are mutually exclusive?

P(A or B) = P(A) + P(B) Signup and view all the answers

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

P(A) + P(A') = 1 Signup and view all the answers

If P(A) = 0.4 and P(B) = 0.3, what is the probability of A and B not occurring, if they are independent?

0.52 Signup and view all the answers

What is the term for events that are mutually exclusive and make up the whole sample space?

Complementary events Signup and view all the answers

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

0 Signup and view all the answers

What is the purpose of the product rule?

To calculate the probability of independent events Signup and view all the answers

What is the symbol for the number of elements in set A?

n(A) Signup and view all the answers

Gr12 Mathematics: Ch 9.1 Identities

Questions and Answers

What is the formula for the probability of an event and its complement?

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

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

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

What does the symbol $A'$ represent in probability?

What is the formula for the probability of two independent events?

What is the condition for the addition rule to simplify to $P(A ext{ or } B) = P(A) + P(B)$?

What is the sample space represented by in probability?

What is the formula for the complementary rule?

What is the condition for two events to be dependent?

What is the condition for two events A and B to be independent?

What is the relationship between mutual exclusivity and independence?

What is the term for events that are mutually exclusive and make up the whole sample space?

What is the purpose of the product rule?

What is the difference between the addition rule and the product rule?

Why is it important to verify if $P(A ext{ and } B) = P(A) imes P(B)$ when testing for independence?

What is the relationship between the probabilities of two events and their union and intersection as expressed by the addition rule?

What is the condition for the addition rule to simplify to P(A or B) = P(A) + P(B)?

What is represented by P(not A)?

When are two events A and B independent?

What can be concluded about two events A and B if P(A and B) = 0?

What is necessary to verify when testing whether two events are independent?

What can be said about the relationship between the probabilities of two mutually exclusive events?

What is the purpose of the complementary rule?

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

If two events A and B are independent, what is the probability of A and B not occurring?

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

What is the term for the set of all possible outcomes in a probability experiment?

If A is an event, what is the notation for the number of elements in set A?

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

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

If two events A and B are mutually exclusive, what is the probability of their intersection?

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

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

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

If A and B are dependent, what can be said about P(A and B)?

What is P(not A) in terms of P(A)?

If P(A or B) = 0.7 and P(A) = 0.4, what is P(B) if A and B are mutually exclusive?

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

If A and B are independent, what is P(A and not B) in terms of P(A) and P(B)?

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

What is the probability of the union of two events A and B, if they are mutually exclusive?

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

If P(A) = 0.4 and P(B) = 0.3, what is the probability of A and B not occurring, if they are independent?

What is the term for events that are mutually exclusive and make up the whole sample space?

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

What is the purpose of the product rule?

What is the symbol for the number of elements in set A?

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