An exceptional bright high school student has applied for two scholarships- a merit scholarship and an athletic scholarship. He estimates the following: . The probability of getting the merit scholarship is 0.36. . The probability of getting the athletic scholarship is 0.33. . 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?

P(at least one) = 0.5054

Step-by-step explanation: from the question

P(merit scholarship) = 0.36

P(athletic scholarship) = 0.33

P(athletic and merit scholarship) = 0.08

A) If p(merit scholarship) = 0.36, p(not getting merit scholarship) = 1 - p(merit scholarship) = 1 - 0.36 = 0.64.

B) P(at least one) = p(merit and not athletic) or p(athletic and not merit) or p(both)

Note p(not athletic) = 1 - 0.33 = 0.67

P(at least one) = (0.36×0.67) + (0.33×0.64) +(0.08)

P(at least one) = 0.2142 + 0.2112 + 0.08

P(at least one) = 0.5054