2. Speeding and alcohol are the most common factors contributing to traffic acci

Question

2. Speeding and alcohol are the most common factors contributing to traffic accidents. For all male drivers under 21 involved in a fatal crash in 2003, 34% were speeding, 25% were intoxicated, and 23% were both speeding and intoxicated. If a fatal crash in 2003 involving a male under 21 is selected at random, a. what is the probability that the driver was speeding or intoxicated? b. what is the probability that the crash was due to neither speeding nor alcohol?

a. what is the probability that the driver was speeding or intoxicated?

b. what is the probability that the crash was due to neither speeding nor alcohol?

Explanation / Answer

Let S shows the event that crash is due to speeding and I shows the event that carsh due to alcohol. From the given information we have

P(S) = 0.34, P(I) = 0.25, P(S and I) = 0.23

a)

By the addition rule, the probability that the driver was speeding or intoxicated is

P(S or I) = P(S) + P(I) - P(S and I) = 0.34 + 0.25 - 0.23 = 0.36

b)

By the complement rule, the probability that the crash was due to neither speeding nor alcohol is

P(neither S nor I) = 1 - P(S or I) = 1 - 0.36 = 0.64

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