Question

In New York City, 45% of all blood donors have type O blood. (Based on data from the Greater New York Blood Program). Find the probability that 5 randomly selected blood donors in NYC all have Group O blood.

Answer 1

Answer:

0.0185 = 1.85% probability that 5 randomly selected blood donors in NYC all have Group O blood.

Step-by-step explanation:

For each donor, there are only two possible outcomes. Either they have type O blood, or they do not. The donors are selected randomly, which means that the probability of a donor having type A blood is independent from other donors. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In New York City, 45% of all blood donors have type O blood.

This means that $p = 0.45$.

Find the probability that 5 randomly selected blood donors in NYC all have Group O blood.

This is $P(X = 5)$ when $n = 5$. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{5,5}.(0.45)^{5}.(0.55)^{0} = 0.0185$

0.0185 = 1.85% probability that 5 randomly selected blood donors in NYC all have Group O blood.