An exceptionally bright high school student has applied for two scholarships: a merit scholarship and an athletic scholarship. He estimates the following probabilities: The probability of getting the merit scholarship is 0.3 The probability of getting the athletic scholarship is 0.6 The probability of getting both scholarships is 0.08.

(a) What is the probability that he does not get the merit scholarship?

(b) What is the probability that he gets at least one of these scholarships?

a) 0.70

b) 0.82

Step-by-step explanation:

a)

Let M be the event that student get merit scholarship and A be the event that student get athletic scholarship.

P (M) = 0.3

P (A) = 0.6

P (M∩A) = 0.08

P (not getting merit scholarships) = P (M') = ?

P (not getting merit scholarships) = 1-P (M)

P (not getting merit scholarships) = 1-0.3

P (not getting merit scholarships) = 0.7

The probability that student not get the merit scholarship is 70%.

b)

P (getting at least one of two scholarships) = P (M or A) = P (M∪A)

P (getting at least one of two scholarships) = P (M) + P (A) - P (M∩A)

P (getting at least one of two scholarships) = 0.3+0.6-0.08

P (getting at least one of two scholarships) = 0.9-0.08

P (getting at least one of two scholarships) = 0.82

The probability that student gets at least one of two scholarships is 82%.