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Chapter 3: Q108SE (page 204)

Speeding linked to fatal car crashes. According to the National Highway Traffic and Safety Administration鈥檚 National Center for Statistics and Analysis (NCSA), 鈥淪peeding is one of the most prevalent factors contributing to fatal traffic crashes鈥� (NHTSA Technical Report, August 2005). The probability that speeding is a cause of a fatal crash is .3. Furthermore, the probability that speeding and missing a curve are causes of a fatal crash is .12. Given speeding is a cause of a fatal crash, what is the probability that the crash occurred on a curve?

Short Answer

Expert verified

The probability is 0.4.

Step by step solution

01

Important formula

The formula is P(A鈭�B)=P(A).P(B|A).

02

The probability that the crash occurred on a curve.

Here, P(G)=0.3=Speeding is a cause of a fatal crash.

P(F|G)=0.12=Speeding and missing a curve are causes of a fatal crash.

P(G鈭�F)=P(G)脳P(F|G)0.12=(0.38)P(F|G)P(F|G)=0.4

Therefore the probability is 0.4.

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Most popular questions from this chapter

Two fair dice are tossed, and the following events are defined:

A: {Sum of the numbers showing is odd.}

B: {Sum of the numbers showing is 9, 11, or 12.}

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Guilt in decision making.Refer to the Journal of Behavioral Decision Making(January 2007) study of theeffect of guilt emotion on how a decision maker focuseson a problem, Exercise 3.48 (p. 183). The results (numberresponding in each category) for the 171 study participantsare reproduced in the table below. Suppose one of the 171participants is selected at random.

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a.Given that the respondent is assigned to the guilty state, what is the probability that the respondent chooses the stated option?

b.If the respondent does not choose to repair the car, what is the probability that the respondent is in the anger state?

c.Are the events {repair the car} and {guilty state }
independent?

Museum management. Refer to the Museum Management and Curatorship (June 2010) study of the criteria used to evaluate museum performance, Exercise 2.14 (p. 74). Recall that the managers of 30 leading museums of contemporary art were asked to provide the performance measure used most often. A summary of the results is reproduced in the table. Performance Measure Number of Museums Total visitors 8 Paying visitors 5 Big shows 6 Funds raised 7 Members 4


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c. Assign reasonable probabilities to the sample points of part b.

d. Refer to parts b and c. Find the probability that both museums use total visitors or funds raised most often as a performance measure.

An experiment results in one of three mutually exclusive events, A, B, or C. It is known that P (A)= .30, P(B)= .55 , and P(C)= .15. Find each of the following probabilities:

a. P(A鈭�B)

b.P(A鈭�C)

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d. P(B鈭�C)

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Consider the experiment depicted by the Venn diagram, with the sample space S containing five sample points. The sample points are assigned the following probabilities:

P (E1) = .20, P (E2) = .30, P (E3)= .30, P (E4) = .10, P (E5) = .10.

a. Calculate P (A), P (B), and P (A鈭�B).

b. Suppose we know that event A has occurred, so that the reduced sample space consists of the three sample points in A鈥攏amely, E1, E2, and E3. Use the formula for conditional probability to adjust the probabilities of these three sample points for the knowledge that A has occurred [i.e., P (Ei/A)]. Verify that the conditional probabilities are in the same proportion to one another as the original sample point probabilities.

c. Calculate the conditional probabilityP (E1/A)in two ways: (1) Add the adjusted (conditional) probabilities of the sample points in the intersection A鈭�B, as these represent the event that B occurs given that A has occurred; (2) use the formula for conditional probability:

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Verify that the two methods yield the same result.

d. Are events A and B independent? Why or why not?
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