Question

Approximately 24% of the calls to an airline reservation phone line result in a reservation being made. (a) Suppose that an operator handles 10 calls. What is the probability that none of the 10 calls result in a reservation? (Give the answer to 3 decimal places.)

Answer 1

0.064 = 6.4% probability that none of the 10 calls result in a reservation.

Explanation:

For each call, there are only two possible outcomes. Either it results in a reservation, or it does not. The probability of a call resulting in a reservation is independent of other calls. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

24% of the calls to an airline reservation phone line result in a reservation being made.

This means that
`p = 0.24`

Suppose that an operator handles 10 calls. What is the probability that none of the 10 calls result in a reservation?

This is P(X = 0) when n = 10. So

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 0) = C_(10,0).(0.24)^(0).(0.76)^(10) = 0.064`

0.064 = 6.4% probability that none of the 10 calls result in a reservation.