Chapter 5: Q 81. (page 330)

Going pro 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 $3$ years. $16$ What is the probability that a high school athlete who plays basketball, baseball, or football competes in college and then goes on to have a pro career of more than $3$ years? Show your work.

Expert verified

The percentage of all adults go to health club at least twice a week is $0.034 %$

Step by step solution

$10 %$ of adults subscribe to a fitness club, with $40 %$ of these members going at least twice a week.

Conditional probability: $P (A \cap B) = P (A / B) \times P (B)$

According to the inquiry, $P (c o l l e g e) = 5 % = 0.05$

$P (m a j o r / c o l l e g e) = 1.7 % = 0.017$

$P (3 + / c o l l e g e \cap m a j o r l e a g u e) = 40 % = 0.40$

Use the following conditional probability definition:

$P (A \cap B) = P (A / B) \times P (B)$

As a result, the following was obtained:

$P (c o l l e g e \cap m a j o r l e a g u e \cap 3 +)$

$= P (3 + c o l l e g e \cap m a j o r l e a g u e) \times P (c o l l e g e / m a j o r l e a g u e)$

$= P (3 + c o l l e g e \cap m a j o r l e a g u e) \times P (m a j o r l e a g u e / c o l l e g e) \times P (c o l l e g e)$

$= 0.40 \times 0.17 \times 0.05 = 0.00034 = 0.034 %$

As a result, a quarter of all individuals visit a health club at least twice a week.

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