Lara R. answered • 05/21/20
Math Major Taking Statistics with 4.0 GPA
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
