Question

A father is questioning the probability his daughter will receive a scholarship. She is a finalist for two different scholarships. The awarding of these scholarships is independent. For the first scholarship (Scholarship A) there are 5 finalists and two scholarships will be awarded. For the second scholarship (Scholarship B) there are also five finalists and one scholarship will be awarded.

5. What is the probability that she will receive Scholarship A and Scholarship B?

6. What is the probability that she will receive at least one scholarship, Scholarship A or Scholarship B?

7. Should she apply for both scholarships or one of the scholarships? If just one, which one? Why?

Answer 1

Here' the answer to the question. Please let me know in case you've doubts.

Lets first calculate probability of the person to receive scholrship A and B.

So ,P(A) = 2C1/5C1 = 2/5
So, P(B) = 1/5

5. P(receive A and B) [P(X and Y) = P(X)*P(Y), if X and Y are independent events]
= P(receive A)*P(receive B)
= (2/5)*(1/5)
= 2/25
= 0.08

6. P(atleast one schorship received)
= 1- P(gets none)
= 1- P(A')*P(B')
= 1- (1 - 2/5)*(1- 1/5)
= 1- (3*4)/25
= 13/25

7. She should apply to the first schorlorship, as she has a higher probability to get it.
P(A) = 2/5 > P(B) = 1/5