Question

A hotel has three elevators. One of them is a freight elevator. When pressing the button, one of the elevators randomly services your floor. If you use the elevators five times what is the probability that you use the freight elevator exactly two times?​

Answer 1

The probability of using the freight elevator exactly two times out of five is approximately 0.329 or 32.9%.

Step-by-step explanation:

To find the probability of using the freight elevator exactly two times out of five, we need to use the concept of combinations. There are a total of 3 elevators and we want to choose 2 of them to be the freight elevator, so the number of combinations is given by the formula C(3, 2) = 3. When pressing the button each time, there is a 1/3 probability of selecting the freight elevator. Therefore, the probability of using the freight elevator exactly two times out of five is given by the formula C(5, 2) * (1/3)^2 * (2/3)^3 = 10 * (1/9) * (8/27) = 80/243, which is approximately 0.329 or 32.9%.