Question 1087848
Question:
Type O blood is found in 44% of Americans. Suppose 7 samples of blood are tested at random. Find the probability that exactly 2 of the tested samples will be Type O.
 
Solution:
The probability is known and constant (small sample, large population), the sample size is known, and sampling is assumed random and independent, each trial is Bernoulli (i.e. type O or not), we can model the situation with binomial distribution, which means
P(x)=C(N,x)(p^x)(1-p)^(N-x)
where,
C(N,x) is number of combinations of selecting x objects out of N.
x is the exact number of success in the sample.
 
For the given situation,
p=0.44
n=7
x=2
so
P(x=2)=C(7,2)(0.44^2)(0.56^5)
=0.2239