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Chapter 5: Q .78. (page 336)

. At the gym Suppose that 10% of adults belong to health clubs, and 40% of these health club members go to the club at least twice a week. Find the probability that a randomly selected adult belongs to a health club and goes there at least twice a week.

Short Answer

Expert verified

Probability for a randomly selected adult belongs to a health club and visit club at least twice a week is0.04.

Step by step solution

01

Step 1:Given information

Adults who subscribe to health clubs make about 10% of the population.

At least twice a week, 40% of these fitness club members visit the facility.

02

Step 2:Calculation

According to general multiplication rule,

P(AandB)=P(A鈭�B)=P(A)脳P(B鈭�A)=P(B)脳P(A鈭�B)

Let

H: adults belong to health clubs

W: health club members go to the club at least twice a week

Now,

The corresponding probabilities:

Probability for the adults belong to health clubs,

P(H)=0.10

Probability for the health club members go to the club at least twice a week,

P(W鈭�H)=0.40

Use the following multiplication rule:

P(HandW)=P(H鈭�W)=P(H)脳P(W鈭�H)

=0.10脳0.40

=0.04

Thus,

Probability for a randomly selected adult belongs to a health club and visit club at least twice a week is0.04.

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Most popular questions from this chapter

Brushing teeth, wasting water? A recent study reported that fewer than half of young adults turn off the water while brushing their teeth. Is the same true for teenagers? To find out, a group of statistics students asked an SRS of 60students at their school if they usually brush with the water off. In the sample, 27students said "Yes." The dotplot shows the results of taking 200SRSS of 60students from a population in which the true proportion who brush with the water off is 0.50.

a. Explain why the sample result (27of the 60students said "Yes") does not give convincing evidence that fewer than half of the school's students brush their teeth with the water off.

b. Suppose instead that 18of the 60students in the class's sample had said "Yes." Explain why this result would give convincing evidence that fewer than 50%of the school's students brush their teeth with the water off.

The partially complete table that follows shows the distribution of scores on the AP庐

Statistics exam for a class of students.

Select a student from this class at random. If the student earned a score of 3 or higher

on the AP庐 Statistics exam, what is the probability that the student scored a 5?

a.0.150b.0.214c.0.300d.0.428e.0.700

Checking independence Suppose C and D are two events such that

P(C)=0.6,P(D)=0.45,and P(C鈭�D)=0.3Are events C and D independent? Justify your answer.

Which one of the following is true about the events 鈥淥wner has a Chevy鈥� and

鈥淥wner鈥檚 truck has four-wheel drive鈥�?

a. These two events are mutually exclusive and independent.

b. These two events are mutually exclusive, but not independent.

c. These two events are not mutually exclusive, but they are independent.

d. These two events are neither mutually exclusive nor independent.

e. These two events are mutually exclusive, but we do not have enough information to determine if they are independent.

Union and intersection Suppose A and B are two events such that P (A)=0.3, P (B)=0.4, and

P (A鈭狟)=0.58. Find P (A鈭〣).
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