Question

question 1 of 10
a food truck sells tacos, burritos, and drinks.
let event ( a = ) a customer buys a taco.
let event ( b = ) a customer buys a drink.
what does ( p(a \text{ or } b)=0.55 ) mean in terms of this problem?
a. buying a taco and buying a drink are mutually exclusive events.
b. the probability that a customer buys a taco, a drink, or both is 55%.
c. the probability that a customer buys neither a taco nor a drink is 55%.
d. the probability that a customer buys both a taco and a drink is 55%.

Explanation:

In probability, \(P(A\ or\ B)\) represents the probability of either event \(A\) (buying a taco) occurring, event \(B\) (buying a drink) occurring, or both events occurring. So, \(P(A\ or\ B) = 0.55\) (or 55%) means the probability that a customer buys a taco, a drink, or both is 55%.

• Option A: There is no information given to suggest that \(A\) and \(B\) are mutually - exclusive (\(P(A\cap B)=0\)).
• Option C: \(P(\text{neither }A\text{ nor }B)=1 - P(A\cup B)\) (by the complement rule). If \(P(A\cup B)=0.55\), then \(P(\text{neither }A\text{ nor }B)=1 - 0.55=0.45\) (or 45%).
• Option D: \(P(A\cap B)\) (probability of both \(A\) and \(B\)) is not the same as \(P(A\cup B)\) (probability of \(A\) or \(B\)). The formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\) shows the difference.

Answer:

B. The probability that a customer buys a taco, a drink, or both is 55%.