Question

Because not all airline passengers show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 120 passengers. The probability that a passenger does not show up is 0.10, and the passengers behave independently. Round your answers to four decimal places (e.g. 98.7654). (a) What is the probability that every passenger who shows up can take the flight

Answer 1

0.9961

Explanation:

Let x be the number of passengers who fail to show up.

Then x is binomially distributed with n = 125 and p = 0.10

we want P[x ≥ 5] = 1 - P[x < 5] = 1 - P[x = 0] - P[x = 1] - P[x = 2] - P[x = 3] - P[x = 4] = 1 - 0.000002 - 0.000026 - 0.000182 - 0.000831 - 0.002817 = 0.996141 ≈ 0.9961

Therefore, the probability that every passenger who shows up can take the flight is 0.9961.