Two buses A and B are scheduled to arrive at a town central bus station at noon. The probus A will be late is `1/5`. The probability that bus B will be late is `7/25`. The probability that the bus B is late given that bus A is late is `9/10`. Then the probabilities:

Options

A. probability that neither bus will be late on a particular dat is `7//10`
B. probability that bus A is late given that bus B is late is `18//28`
C. probability that at least ne bus is late is `3//10`
D. probability that at least one bus is in time is `4//5`

Answer

A, B, C

Explanation

(1) `P(A)=1/5,P(B) =7/25,P(B//A)=9/10`
`P(barAnnbarB)=1-P(AuuB)`
`=1-[P(A)+P(B)-P(AnnB)]`
`=1-[(1)/(5)+(7)/(25)-P(A)P(B//A)]`
`=1-[(1)/(5)+(7)/(25)-1/5xx7/25]=7/10`
(2) `P(A//B)=(P(AnnB))/(P(B))`
`=(P(A)P(B//A))/(P(B))=(1/5xx9/10)/(7/25)`
`=9/50xx25/7=9/14=18/28`
(3) `P(AuuB)=P(A)+P(B)-P(A)+P(B)-P(AnnB)`
`" "=P(A)+P(B)-P(A)P(B//A)`
`=1/5+7/25-1/5xx9/10=41/50`