Question

A person with type O blood can donate red blood cells to anybody because type O blood is the universal blood type. About 44% of the US population has type O blood. University High held a blood drive where 50 students donated blood.

Part A: What is the probability that exactly 25 of the students had type O blood? (5 points)

Part B: What is the probability that at least 25 of the students had type O blood? (5 points)

Answer 1

Here you must use a Binomial probability. Here's how I know:
-There is a probability of success of 44% being O blood
-There are essentially 50 trials (students)
-The result of one student is independent from the other.

Note that Binomial probabilities are in the form
\[P(X=x)=\text{B(n,p,k)}={n\choose k}p^k(1-p)^{n-x}\]
where n=trials, k=number of successes, p=probability of success
Part A
Here you have to run a binomial probability distribution, with n=50, k=25, and p=0.44.
\[{P(X=25)=\text{B(50, 0.44, 24)}={50\choose 25}(0.44)^{25}(1-0.44)^{50-25}}\]

Part B.
Here, "at least 25" translates to P(X≥25)...i.e., a Binomial Wizardulative distribution....
\[{P(X≥25)=\sum_{n=25}^{50}{50\choose n}(0.44)^{n}(1-0.44)^{50-n}}\]


You'll probably need to do these questions using your calculator.

Answer 2

Sorry the filter said wizardulative. Part B is an example of a binomial cumulative distribution