Blood types: The blood type o negative is called the "universal donor" type, because it is the only blood type that may safely be transfused into any person Therefore, when someone needs a transfusion in an emergency and their blood type cannot be determined, they are given type o negative blood. For this
reason, donors with this blood type are crucial to blood banks. Unfortunately, this blood type is fairly rare; according to the Red Cross, only 7% of U. S.
residents have type o negative blood. Assume that a blood bank has recruited 18 donors. Round the answers to four decimal places
Part 1 of 3
(a) What is the probability that three or more of them have type o negative blood?
The probability that three or more of them have type o negative blood is
х
Part 2 of 3
(b) What is the probability that fewer than five of them have type o negative blood?
The probability that fewer than five of them have type o negative blood is
х
Part 3 of
(©) Would it be unusual f none of the donors had type o negative blood?
be unusual if none of the donors had type o negative blood since the probability is
X
It choose one) Y
would
would not

a) The probability that fewer than five of them have type o negative blood is 0.1275

b) The probability that fewer than five of them have type o negative blood is 0.9933

c) 0.2708 probability of no donors with type o negative blood. This probability is higher than 0.05, so it would not be unusual having none of the donors with type o negative blood.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they have type o negative blood, or they do not. The probability of a person having type o negative blood is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

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

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

And p is the probability of X happening.

7% of U.S. residents have type o negative blood.

This means that

18 donors.

This means that

(a) What is the probability that three or more of them have type o negative blood?

Either less than three have, or at least three do. The sum of the probabilities of these events is 1. So

We want

So

In which

The probability that fewer than five of them have type o negative blood is 0.1275

(b) What is the probability that fewer than five of them have type o negative blood?

The probability that fewer than five of them have type o negative blood is 0.9933.

c) Would it be unusual f none of the donors had type o negative blood?

0.2708 probability of no donors with type o negative blood. This probability is higher than 0.05, so it would not be unusual having none of the donors with type o negative blood.

a negative exponent is translated as follows:

so, we have