Question

Thirty-nine percent of people in a certain country like to cook and 69% of people in the country like to shop, while 19% enjoy both activities. What is the probability that a randomly selected person in the country enjoys cooking or shopping or both? The probability that a randomly selected person in the country enjoys cooking or shopping or both is (Type an integer or a decimal. Do not round.)

Answer 1

The probability that a randomly selected person enjoys cooking or shopping or both is 0.89 or 89%, calculated using the principle of inclusion-exclusion for two sets.

Step-by-step explanation:

The probability that a randomly selected person in the country enjoys cooking or shopping or both can be calculated using the principle of inclusion-exclusion for two sets. This principle states that for any two events A and B, the probability of A or B occurring is given by:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

According to the question, 39% of people like to cook (P(Cooking) = 0.39), 69% like to shop (P(Shopping) = 0.69), and 19% enjoy both activities (P(Cooking ∩ Shopping) = 0.19). Substituting these values into the formula:

P(Cooking ∪ Shopping) = 0.39 + 0.69 - 0.19 = 0.89

So, the probability that a randomly selected person enjoys cooking or shopping or both is 0.89, i.e., 89%.