AP Statistics · Topic 4.4

Mutually Exclusive Events Practice

Part of Probability, Random Variables, and Probability Distributions.(VAR-4.B)

Practice questions

4

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Sample questions

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Sample 1difficulty 2/5
$For mutually exclusive A, B: P(A or B) =$
- A
  $1 - P(A)P(B)$
- B
  $P(A) \cdot P(B)$
- C
  $P(A) + P(B) - P(A\capB)$
- D
  $P(A) + P(B)$
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Why
$Mutually exclusive \Rightarrow P(A\capB) = 0.$
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Sample 2difficulty 2/5
$Events A and B are mutually exclusive with P(A) = 0.30 and P(B) = 0.25.$
$What is P(A or B)?$
- A
  $0.05$
- B
  $0.30$
- C
  $0.075$
- D
  $0.55$
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Why
$Mutually exclusive: P(A and B) = 0. So P(A or B) = 0.30 + 0.25 = 0.55.$
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Sample 3difficulty 3/5
$For 3 mutually exclusive events with probabilities 0.2, 0.3, 0.4, P(none) =$
- A
  $0.2$
- B
  $0.5$
- C
  $0.1$
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- D
  $0.9$
Why
$P(any) = 0.9; P(none) = 1 - 0.9 = 0.1.$
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Sample 4difficulty 3/5
$Two events A and B both have positive probability and are mutually exclusive.$
$Which statement must be true?$
- A
  $P(A and B) = P(A)P(B)$
- B
  $P(A) + P(B) = 1$
- C
  $A and B cannot be independent$
  check_circle
- D
  $A and B must be independent$
Why
$If mutually exclusive with positive probabilities, P(A and B) = 0 but P(A)P(B) > 0, so they cannot be independent.$
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