EXAMPLE 4.46

High school athletes and professional careers. Only 5% of male high school basketball, baseball, and football players go on to play at the college level. Of these, only 1.7% enter major league professional sports. About 40% of the athletes who compete in college and then reach the pros have a career of more than three years. Define these events:

A = {competes in college}

B = {competes professionally}

C = {pro career longer than 3 years}

What is the probability that a high school athlete competes in college and then goes on to have a pro career of more than three years? We know that

P(A) = 0.05

P(B | A) = 0.017

P(C | A and B) = 0.4

Therefore, the probability we want is

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

= 0.05 × 0.017 × 0.4 = 0.00034

Only about 3 of every 10,000 high school athletes can expect to compete in college and have a professional career of more than three years. High school students would be wise to concentrate on studies rather than on unrealistic hopes of fortune from pro sports.