Question

Data compiled by the Highway Patrol Department regarding the use of seat-belts by drivers in a certain area after the passage of a compulsory seat-belt law are shown in the accompanying table. (Round your answers to three decimal places.) 

(a) If a driver in that area is stopped for a moving violation, what is the probability that he or she will have a seat-belt on? 

(b) If a driver in that area is stopped for a moving violation, what is the probability that he or she will not have a seat-belt on?

Answer 1

Bayes' Theorem: P(A | B) = P(A & B)/P(B)

a) P(seat belt on | stopped for moving violation) = P(seat belt on and stopped for moving violation)/P(stopped for moving violation)

= (73x0.4)/(73x0.4 + 27x0.5)

= 0.684

b) P(will not have seat belt on | stopped for moving violation) = 1 - 0.684

= 0.316