Respuesta :
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.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In New York City, 45% of all blood donors have type O blood.
This means that [tex]p = 0.45[/tex].
Find the probability that 5 randomly selected blood donors in NYC all have Group O blood.
This is [tex]P(X = 5)[/tex] when [tex]n = 5[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.45)^{5}.(0.55)^{0} = 0.0185[/tex]
0.0185 = 1.85% probability that 5 randomly selected blood donors in NYC all have Group O blood.
