Question

Item 13

A student is applying to two different agencies for scholarships. Based on the student’s academic record, the probability that the student will be awarded a scholarship from Agency A is 0. 55 and the probability that the student will be awarded a scholarship from Agency B is 0. 40. Furthermore, if the student is awarded a scholarship from Agency A, the probability that the student will be awarded a scholarship from Agency B is 0. 60. What is the probability that the student will be awarded at least one of the two scholarships?

Answer 1

Let A be the event that the student is awarded a scholarship from Agency A, and let B be the event that the student is awarded a scholarship from Agency B. We want to find P(A or B), the probability that the student is awarded at least one of the two scholarships.

We can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

We know that P(A) = 0.55, P(B) = 0.40, and P(B|A) = 0.60. To find P(A and B), we can use the formula:

P(A and B) = P(B|A) * P(A)

P(A and B) = 0.60 * 0.55 = 0.33

Now we can substitute into the formula for P(A or B):

P(A or B) = 0.55 + 0.40 - 0.33 = 0.62

Therefore, the probability that the student will be awarded at least one of the two scholarships is 0.62.