Question

You have gone back to that famous European beach where 36 of the 60 other visitors speak English. If you randomly meet three people on the beach, what is the probability that exactly two of them speak English?

Answer 1

To find the probability that exactly two out of three randomly selected people speak English, we need to use the binomial probability formula.

Step-by-step explanation:

To find the probability that exactly two out of three randomly selected people speak English, we need to use the binomial probability formula. The formula is: P(X = k) = (n choose k) * p^k * (1 - p)^(n - k), where n is the total number of trials, k is the number of successes, and p is the probability of success.

In this case, we have n = 3 (because we are randomly selecting three people), k = 2 (because we want exactly two people to speak English), and p = 36/60 (because 36 out of 60 visitors speak English). Now we can calculate the probability:

P(X = 2) = (3 choose 2) * (36/60)^2 * (1 - 36/60)^(3 - 2) = 3 * (36/60)^2 * (24/60) = 0.432.