SOLUTION: 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.

Question 1087848: 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.
Found 2 solutions by rothauserc, mathmate:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
use the binomial probability formula
:
Probability (P) ( k successes in n trials ) = nCk * p^k * (1-p)^(n-k), where
nCk = n! / (k! * (n-k)!)
:
P ( exactly 2 have type O blood out of 7 trials ) = 7C2 * (0.44)^2 * (1-0.44)^(7-2) = 0.2239 approx 0.22
:
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P of exactly 2 with type O out of 7 trials = 0.22
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:

Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
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
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