Question

64% of all drivers use seat belts, while the remaining 36% do not use seat belts....

64% of all drivers use seat belts, while the remaining 36% do not use seat belts. Drivers using a seat belt have 0.2% chance to be stopped for a moving violation. In contrast, drivers that do not use a seat belt have a 0.5% chance to be stopped for a moving violation. A random driver is stopped for a moving violation, what is the probability that the driver will have a seat belt?

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Answer #1

Baye's Theorem

P(A | B) = P(A and B)/P(B)

P(driver will have a seat belt | stopped for a moving violation) = P(driver will have a seat belt and stopped for a moving violation) / P(stopped for a moving violation)

= 0.64x0.002/(0.64x0.002 + 0.36x0.005)

= 0.4156

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