Question

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?

A. 0.60
B. 0.62
C. 0.71
D. 0.73
E. 0.95

Answer 1

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

Step-by-step explanation:

To calculate the probability that the student will be awarded at least one of the two scholarships, we need to consider the probability of receiving each scholarship and the combined probability. The probability of getting a scholarship from Agency A is 0.55, and from Agency B is 0.40. If the student gets a scholarship from Agency A, the probability of also getting one from Agency B is 0.60. We can calculate the probability of getting at least one scholarship using the formula for the union of two events: P(A or B) = P(A) + P(B) - P(A and B).

First, we need to find P(A and B), which is the probability of getting both scholarships. Since getting a scholarship from B given A is 0.60, P(A and B) would be P(A) multiplied by P(B|A):

P(A and B) = P(A) × P(B|A) = 0.55 × 0.60 = 0.33

Now, we can find the probability of getting at least one scholarship:

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

The correct answer is B. 0.62, which is the probability that the student will be awarded at least one of the two scholarships.