According to the National Highway Safety Administration, for all male drivers in

Question

According to the National Highway Safety Administration, for all male drivers involved in a fatal crash in 2003, it was found that 34% were speeding, 25% were intoxicated, and 23% were both speeding and intoxicated. Suppose that a fatal crash involving a male driver under 21 is selected at random. What is the probability that the driver

a) was speeding or intoxicated?

b) was not speeding and not intoxicated?

c) was speeding given that he was not intoxicated?

* I do not know how to approach these questions. Please, I need a complete explanation on how to do this with formulas and the critical thinking behind it to properly analyze the problem. I need this to practice for my Final Today! *

Explanation / Answer

Let A : Male drivers found speeding

B : Male drivers who were intoxicated

P( A ) = 0.34

P(B) = 0.25

P( A and B) = 0.23

a.) P( A or B) = P(A) + P(B) - P( A and B)

= 0.34 + 0.25 + 0.23

= 0.36

B.) P( not A and not B)

= 1 - P(A or B)

= 1 - 0.36

= 0.64

c.) P( A and not B)

= P(A) - P( A and B)

= 0.34 - 0.23

= 0.11

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