# Math Help - Probability word question

1. ## Probability word question

Hi, I have some idea of how to figure this one out, but not too sure.

In February 2006, the major U.S. airline with the fewest delays was US Airways, for which 79.2% of their flights arrived on time. Assume that the event that a given flight arrives on time is independent of the event that another flight arrives on time.

a) Chrissy plans to take four separate flights next month on US Airways. Assuming that the airline has the same on-time performance as in February 2006, what is the probability that all four flights arrive on time?

b) Discuss how realistic it is to assume that the on-time arrivals of the different flights are independent.

So it's finding the probability that all 4 flights arrive on time given that they have a 79.2% performance rate of arriving on time. So since they are independent of one another, it would be 0.792 * 0.792 * 0.792 * 0.792. Is this right?

Thanks very much..

2. Use the binomial theorem here, it might give you the same answer.

Where n is the number of flights and p is the probability, you have k=4 and

$\displaystyle P(X=k) = ^nC_k p^k (1-p)^{n-k} \implies P(X=4) = ^4C_4 (0.792)^4 (1-0.792)^{n-k}$

3. yup it gave the same answer: apx. 0.393