Question

Forty percent of passengers with a certain airline prefer a window seat. The probability that exactly two of the next ten person buying a ticket with this airline will prefer a window seat is about: Give your answer correct to 4 decimals.

Answer 1

The probability that exactly two of the next ten persons buying a ticket with the airline will prefer a window seat is approximately 0.1209.

Step-by-step explanation:

To find the probability that exactly two of the next ten persons buying a ticket with the airline will prefer a window seat, we can use the binomial probability formula.

The formula is:

P(X = k) = C(n, k) * pk * (1 - p)(n-k)

Where:

• P(X = k) is the probability of having exactly k successes
• n is the number of trials (in this case, 10 people)
• p is the probability of success (in this case, 0.4)
• C(n, k) is the number of combinations of n objects taken k at a time

Substituting the values into the formula:

P(X = 2) = C(10, 2) * 0.42 * (1 - 0.4)(10-2)

Simplifying the equation gives:

P(X = 2) = 45 * 0.42 * 0.68

Calculating the value gives approximately 0.1209. Therefore, the probability that exactly two of the next ten persons buying a ticket with the airline will prefer a window seat is approximately 0.1209.