Gr12 Mathematics: Ch 9.1 Identities
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Questions and Answers

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

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

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

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

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

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

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

What is the sample space represented by in probability?

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

What is the formula for the complementary rule?

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

What is the condition for two events to be dependent?

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

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

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

What is the relationship between mutual exclusivity and independence?

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

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

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

What is the purpose of the product rule?

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

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

<p>The addition rule is for the union of two events, while the product rule is for the intersection of two events (D)</p> 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?

<p>To ensure that the events are independent (D)</p> 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?

<p>The probability of the union is the sum of the probabilities of the events minus the probability of their intersection. (C)</p> 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)?

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

What is represented by P(not A)?

<p>The probability of the complement of event A. (B)</p> Signup and view all the answers

When are two events A and B independent?

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

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

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

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

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

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

<p>The probability of their union is the sum of their probabilities. (B)</p> Signup and view all the answers

What is the purpose of the complementary rule?

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

What is 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

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

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

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

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

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

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

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

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

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

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

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

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

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

<p>No condition is necessary (B)</p> 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)?

<p>0.15 (C)</p> Signup and view all the answers

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

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

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

<p>1 - P(A) (A)</p> 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?

<p>0.3 (A)</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 (A)</p> 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>P(A)(1 - P(B)) (A)</p> Signup and view all the answers

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

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

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

<p>P(A) + P(A') = 1 (B)</p> 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?

<p>0.52 (B)</p> Signup and view all the answers

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

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

If 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 product rule?

<p>To calculate the probability of independent events (B)</p> Signup and view all the answers

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

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

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