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?

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

Answer 1

To find the probability that exactly 25 students had type O blood, use the binomial probability formula. To find the probability that at least 25 students had type O blood, calculate the sum of individual probabilities.

Step-by-step explanation:

In order to find the probability that exactly 25 of the students had type O blood, we can use the binomial probability formula. The probability of an individual student having type O blood is 0.44. Using the binomial probability formula with n = 50 and p = 0.44, we can calculate:

P(25 students with type O blood) = C(50, 25) * (0.44)^25 * (0.56)^25

In order to find the probability that at least 25 of the students had type O blood, we need to calculate the sum of the probabilities of having 25, 26, 27, ..., 50 students with type O blood. This can be done by calculating the individual probabilities and adding them up.

Answer 2

Part A.

k= 25

p= 44% = 0.44

n= 50

P(x = k) = (nk) p^k (1 - p) ^n - k

P(x = 25) = (50 25) (0.44)^25 (1 - 0.44) ^50 - 25

50!/25!(50 - 25)!

50!/25!(25)! = 1.264106 x 1014

P(x=25) = (1.264106 x 1014)(0.44)^25(0.56)^25

= 0.07812

= 7.8% probability that exactly 25 students have type O blood

Part B.

Do the same math you did above. Just replace 25 with 26 and 27 :)

25 = 7.8% probability

26 = 0.01851

= 1.8% probability

27 = 0.00405

= 0.4% probability