Question

question 4 of 25
a pet store sells mice, reptiles, and birds.
let event ( a = ) a customer buys a mouse.
let event ( b = ) a customer buys a bird.
what does ( p(a \text{ or } b)=0.15 ) mean in terms of this problem?
a. the probability that a customer buys neither a mouse nor a bird is
15%.
b. the probability that a customer buys either a mouse or a bird is
15%.
c. the probability that a customer buys both a mouse and a bird is
15%.
d. buying a mouse and buying a bird are mutually exclusive events.

Explanation:

In probability, \(P(A\ or\ B)\) represents the probability that either event \(A\) (customer buys a mouse) or event \(B\) (customer buys a bird) occurs. Given \(P(A\ or\ B)=0.15 = 15\%\), it means the probability of either \(A\) or \(B\) happening.

• Option A: \(P(A\ or\ B)\) is not about neither event, so A is wrong.
• Option B: Correctly interprets \(P(A\ or\ B)\) as the probability of either \(A\) (mouse) or \(B\) (bird) purchase.
• Option C: \(P(A\ or\ B)\) is not for both events simultaneously; \(P(A\ and\ B)\) would be for that. So C is wrong.
• Option D: \(P(A\ or\ B)\) value alone doesn't prove mutual - exclusivity (which requires \(P(A\ and\ B) = 0\)). So D is wrong.

Answer:

B. The probability that a customer buys either a mouse or a bird is 15%.