Question

Information was collected on those who attended the opening of a new movie. The analysis found that 56 percent of the moviegoers were female, 26 percent were under age 25, and 17 percent were females under the age of 25. Find the probability that a moviegoer is either female or under age 25.Information was collected on those who attended the opening of a new movie. The analysis found that 56 percent of the moviegoers were female, 26 percent were under age 25, and 17 percent were females under the age of 25. Find the probability that a moviegoer is either female or under age 25.

Answer 1

0.65 = 65%

Explanation:

56% of the moviegoers were female: P(F) = 0.56

26% were under age 25: P(25-) = 0.26

17% were females under the age of 25: P(F ∩ 25-) = 0.17

Probability that a moviegoer is either female or under age 25: P(F ∪ 25-) = ?

We know that P (A ∪ B) = P(A) + P(B) - P(A ∩ B), so:

P(F ∪ 25-) = P(F) + P(25-) - P(F ∩ 25-) = 0.56 + 0.26 - 0.17 = 0.65