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

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

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) = (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.