Question

Suppose the probability that a U.S. resident has traveled to Canada is 0.18, to Mexico is 0.09, and to both countries is 0.04. What's the probability that an American chosen at random went to either Canada or Mexico?

Answer 1

The probability that an American chosen at random has traveled to either Canada or Mexico is 0.23, or 23%, using the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Step-by-step explanation:

To calculate the probability that an American chosen at random has traveled to either Canada or Mexico, we use the formula for the probability of the union of two events, which is P(A ∪ B) = P(A) + P(B) - P(A ∩ B). In this case, A is the event of traveling to Canada, and B is the event of traveling to Mexico. Given: P(A) = Probability of traveling to Canada = 0.18, P(B) = Probability of traveling to Mexico = 0.09, P(A ∩ B) = Probability of traveling to both Canada and Mexico = 0.04

The probability that an American has traveled to either Canada or Mexico is: P(A ∪ B) = P(A) + P(B) - P(A ∩ B), P(A ∪ B) = 0.18 + 0.09 - 0.04, P(A ∪ B) = 0.23. Therefore, the probability that a U.S. resident has traveled to either Canada or Mexico is 0.23, or 23%.