On a Saturday night, 20%of all drivers in U.S.A. are under the influence of alcohol. The probability that a drive under the influence of alcohol will have an accident is 0.001. The probability that a sober drive will have an accident is 0.00. if a car on a Saturday night smashed into a tree, the probability that the driver was under the influence of alcohol is `3//7` b. `4//7` c. `5//7` d. `6//7`

Options

A. `3//7`
B. `4//7`
C. `5//7`
D. `6//7`

Answer

C

Explanation

A: car met with an accident
`B_(1):` driver was alcoholic, `P(B_(1))=1//5`
`B_(2):` driver was sober, `P(B_(2))=4//5`
`P(A//B_(1))=0.001,P(A//B_(2))=0.0001`
`P(B_(1)//A)((0.2)(0.001))/((0.2)(0.001)+(0.8)(0.0001))=5//7`