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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

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)

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e. Are B and C independent events? Explain.

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Investing in stocks. From a list of 15 preferred stocks recommended by your broker, you will select three to invest in. How many different ways can you select the three stocks from the 15 recommended stocks?

Consider two events A and B, withP(A)=.1,P(B)=.2,andP(A鈭�B)=0

a.Are A and B mutually exclusive?

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Appeals of federal civil trials. The Journal of the American Law and Economics Association (Vol. 3, 2001) publishedthe results of a study of appeals of federal civil trials. Thefollowing table, extracted from the article, gives a breakdownof 2,143 civil cases that were appealed by either theplaintiff or the defendant. The outcome of the appeal, aswell as the type of trial (judge or jury), was determined foreach civil case. Suppose one of the 2,143 cases is selected

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