Answer to Question #95785 in Statistics and Probability for Sam

Question

Worldwide, the sports industry has become synonymous with big business. It has been estimated by the United Nations that sports account for nearly 3% of global economic activity. Professional football under the management of the National Football League (NFL) is one of the most profitable sport in the world. With multi-million-dollar signing contracts, the economic appeal of pursuing a career as a professional sports athlete is unquestionably strong. But what are the realities? Only 6.5% of high school football players go on to play at the college level. Of these, only 1.2% will play in the NFL. About 40% of the NFL players have a career of more than 3 years. Would high school football players be wise to concentrate on studies rather than unrealistic hopes of fortune from pro football? To answer this question, find the probability that a high school football player competes in college and then goes on to have an NFL career of more than 3 years.

Answer 1

Using the formula for conditional probabilty:

P(player competes in college and then goes on to have an NFL career of more than 3 years | high school football player) = P(play at the college level | play in high school) * P(play in the NFL | play at the college level) * P(a career of more than 3 years | play in the NFL) = 0.065 * 0.012 * 0.4 = 0.000312