Probability Question

Question

There is a 75 percent probablitly that an individual pea will have green pod.  What is the probability that among the nine, no more than 1 has a green pod.  Is it unusual to get more than one pea with a green pod.  Why or why not.

Answer 1

The probability of one pea having a green pod is 0.75 and therefore the probability of the pea not having a green pod is 1-0.75=0.25. The probability of none of the 9 having a green pod is 0.25^9=0.0000038. The probability of just one having a green pod is 9*0.25^8*0.75=0.000103, that is, 8 without a green pod and one with. There are 9 ways this can happen because the pea with the pod can be any one of the nine peas. Add these two probabilities together: 0.0001068 approx. So this is a small probability which means that it's not likely that we would get at most one pea with a pod. Therefore it is highly likely that in 9 peas more than 1 would contain a pod. It would be unusual to get at most one pea with a pod, and it would be usual to get more peas with a pod.