Inactive Tutor answered • 05/21/20
This question deals with binomial probability. Recall that binomial probability deals with ”x” successes on “n” repeated trials which has two possible outcomes (often called a “success” and “failure”). In this example, choosing someone with Type O blood is a “success” and choosing someone with any other blood type is a “failure.” These are the only two possible outcomes.
The formula for binomial probability is
n! / (k! (n-k)!) * [p^k * q^n-k]
n=number of trials
k=number of successes
p=probability of success
q=probability of failure
so let’s apply the formula to part a). The question is asking that out of six people, what is the probability that none have type O blood. There are six people, so there are six ‘trials.’ We want to know the probability that zero of them have type O blood, so our number of successes is zero.
n! / (k! (n-k)!) * [p^k * q^n-k]
6! / (0! (6-0)!) * [0.45^0 * 0.55^6-0]
0.02768
For part b), remember that “at least one” is the same thing as “1 - never at all.” Since we’ve already calculated the probability of zero people having Type O blood in part A, all we have to do is subtract our answer from one.
1-0.02768 = 0.97232
