(9/15)=(15C9)(.75)^9(.15)^(15-7)

math 120 prob and stats

pls help asap

Explanation:

You're on the right track. The 15 C 9 refers to the nCr combination formula which is built into the binomial probability.

The 0.75^9 is also correct

The 0.15^(15-7) portion is not correct. That 0.15 should be 0.25 so it adds to 0.75 to get 1.00 or just 1

Also, the (15-7) portion should be (15-9)

So here's how the steps should look

B(x) = probability of getting a certain x value in a binomial distribution

B(x) = (nCx)*(p)^(x)*(1-p)^(n-x)

B(9) = (15C9)*(0.75)^(9)*(1-0.75)^(15-9)

B(9) = 5005*(0.75)^(9)*(0.25)^(6)

B(9) = 0.09174776729197

B(9) = 0.0917

The probability of getting exactly 9 flights on time is roughly 0.0917

This applies to one trial.

In 100 trials, we expect about 100*0.0917 = 9.17 = 9 flights to be on time.

It's a coincidence that we get a final answer of 9 which matches with the other 9 mentioned in the instructions. This won't always be the case.