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Chapter 3: Q.123. (page 231)

Use the following information to answer the next two exercises. The percent of licensed U.S. drivers (from a recent year) that are female is \(48.60\). Of the females, \(5.03%\) are age \(19\) and under; \(81.36%\) are age \(20鈥�64; 13.61%\) are age \(65\) or over. Of the licensed U.S. male drivers, \(5.04%\) are age \(19\) and under; \(81.43%\) are age \(20鈥�64; 13.53%\) are age \(65\) or over.

Compute the following:

a. Construct a table or a tree diagram of the situations.

b. Find \(P\)(driver is female)

c. Find \(P\)(driver is age \(65\) or over|driver is female).

Short Answer

Expert verified

Part a. The table that represents the given situation is,


 \(<20\) \(20-64\) \(>64\)
 Totals
Female \(0.0244\) \(0.3954\) \(0.0661\) \(0.486\)
Male \(0.0259\) \(0.4186\) \(0.0695\) \(0.514\)
Totals \(0.0503\) \(0.8140\) \(0.1356\) \(1\)

Part b. \(P\)(driver is female)\(=0.486\)

Part c. \(P\)(driver is age \(65\) or above| driver is female)\(=0.1361\)

Step by step solution

01

Part a. Step 1. Given information

The percent of licensed U.S driver that are female is \(48.60\). Of the females \(5.03%\) are age \(19\) and under, \(81.36%\) are age \(20-64 ,13.61%\) are age \(65\) or over. Of the licensed U.S male drivers, \(5.04%\) are age \(19\) and under, \(81.43%\) are age \(20-64 ,13.53%\) are age \(65\) or over.

02

Part a. Step 2. Calculation

The table representation is as follows:


 \(<20\) \(20-64\) \(>64\)
 Totals
Female \(0.0244\) \(0.3954\) \(0.0661\) \(0.486\)
Male \(0.0259\) \(0.4186\) \(0.0695\) \(0.514\)
Totals \(0.0503\) \(0.8140\) \(0.1356\) \(1\)
03

Part b. Step 1. Calculation

The table representation is as follows:


 \(<20\) \(20-64\) \(>64\)
 Totals
Female \(0.0244\) \(0.3954\) \(0.0661\) \(0.486\)
Male \(0.0259\) \(0.4186\) \(0.0695\) \(0.514\)
Totals \(0.0503\) \(0.8140\) \(0.1356\) \(1\)

From above table, the probability the driver is female is given as

\(P\)(driver is female)\(=0.486\)

04

Part c. Step 1. Calculation

The table representation is as follows:


 \(<20\) \(20-64\) \(>64\)
 Totals
Female \(0.0244\) \(0.3954\) \(0.0661\) \(0.486\)
Male \(0.0259\) \(0.4186\) \(0.0695\) \(0.514\)
Totals \(0.0503\) \(0.8140\) \(0.1356\) \(1\)

From above table, we have

\(P\)(driver is female)\(=0.486\)

The probability the driver is age 65 or above given that the driver is female is given as

\(P\)(driver is age \(65\) or above| driver is female)\(=\frac{0.0661}{0.486}\)

\(P\)(driver is age \(65\) or above| driver is female)\(=0.1361\)

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Most popular questions from this chapter

Use the following information to answer the next 12exercises. The graph shown is based on more than 1,70,000interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score.

Find the probability that an Emotional Health Index Score is between 80.5 and 82?

Forty-eight percent of all Californians registered voters prefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55%prefer life in prison without parole over the death penalty for a person convicted of first degree murder. 37.6%of all Californians are Latino. In this problem, let: 鈥� C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder. L = Latino Californians. Suppose that one Californian is randomly selected.

Find P(L AND C).

A student goes to the library. Let events B = the student checks out a book and D = the student checks out a DVD. Suppose that P(B) = 0.40, P(D) = 0.30 and P(B AND D) = 0.20.

a. Find P(B|D).

b. Find P(D|B).

c. Are B and D independent?

d. Are B and D mutually exclusive?

Suppose that you randomly draw two cards, one at a time, without replacement.

G1= first card is green

G2= second card is green

a. Draw a tree diagram of the situation.

b. Find P(G1ANDG2).

c. Find P(at least one green).

d. Find P(G2|G1).

e. Are G2 and G1 independent events? Explain why or why not

1994, the U.S. government held a lottery to issue 55000Green Cards (permits for non-citizens to work legally in the U.S.). Renate Deutsch, from Germany, was one of approximately 6.5million people who entered this lottery. Let G = won green card.

a. What was Renate鈥檚 chance of winning a Green Card? Write your answer as a probability statement.

b. In the summer of 1994, Renate received a letter stating she was one of 110,000finalists chosen. Once the finalists were chosen, assuming that each finalist had an equal chance to win, what was Renate鈥檚 chance of winning a Green Card? Write your answer as a conditional probability statement. Let F = was a finalist.

c. Are G andF independent or dependent events? Justify your answer numerically and also explain why.

d. Are G and F mutually exclusive events? Justify your answer numerically and explain why.
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