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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, only1.7% enter major league professional sports. About 40% of the athletes who compete in college and then reach the pros have a career of more than3 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.

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given Information

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

02

Step 2. Concept Used

Conditional probability: P(A鈭�B)=P(A/B)脳P(B)

03

Step 3. Calculation

According to the inquiry, P(college)=5%=0.05

P(major/college)=1.7%=0.017

P(3+/college鈭�majorleague)=40%=0.40

Use the following conditional probability definition:

P(A鈭�B)=P(A/B)脳P(B)

As a result, the following was obtained:

P(college鈭�majorleague鈭�3+)

=P(3+college鈭�majorleague)脳P(college/majorleague)

=P(3+college鈭�majorleague)脳P(majorleague/college)脳P(college)

=0.40脳0.17脳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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Most popular questions from this chapter

Sampling senators Refer to Exercise 67. Are events D and F independent? Justify your answer.

Free throws The figure below shows the results of a basketball player shooting several free throws. Explain what this graph says about chance behavior in the short run and long run.

Mac or PC? A recent census at a major university revealed that 40% of its students mainly used Macintosh computers (Macs). The rest mainly used

PCs. At the time of the census, 67% of the school鈥檚 students were undergraduates. The rest were graduate students. In the census, 23%of the respondents were graduate students who said that they used PCs as their

primary computers. Suppose we select a student at random from among those who were part of the census and learn that the student mainly uses a Mac.

Find the probability that this person is a graduate student. Show your work.

Mac or PC? A recent census at a major university revealed that40% of its students primarily used Macintosh computers (Macs). The rest mainly used

PCs. At the time of the census, 67% of the school鈥檚 students were undergraduates. The rest were graduate students. In the census, 23% of respondents were graduate students who said that they used PCs as their

main computers. Suppose we select a student at random from among those who were part of the census.

(a) Assuming that there were 10,000 students in the census, make a two-way table for this chance process.

(b) Construct a Venn diagram to represent this setting.

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(d) Find the probability of the event described in (c). Explain your method.

An unenlightened gambler

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heavily on black at the next spin. Asked why he explains that black is 鈥渄ue by the law of averages.鈥� Explain to the gambler what is wrong with this reasoning.

(b) After hearing you explain why red and black are still equally likely after five reds on the roulette wheel, the gambler moves to a poker game. He is dealt five straight red cards. He remembers what you said and assumes that the next card dealt in the same hand is equally likely to be red or black. Is the gambler right or wrong, and why?
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