ProbabilityMedium
Question
Two buses A and B are scheduled to arrive at a town central bus station at noon. The probability that bus 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
(i) neither bus will be late on a particular day and
(ii) bus A is late given that bus B is late, are respectively
(i) neither bus will be late on a particular day and
(ii) bus A is late given that bus B is late, are respectively
Options
A.2/25 and 12/28
B.18/25 and 22/28
C.7/10 and 18/28
D.12/25 and 2/28
Solution
P(A) ; denote the probability that bus A will be late.
P(B) ; denote the probability that bus B will be late.
P(A) =
, P(B) = 
P
⇒ P(A ∩ B)
(i) P(
∩ 
) = 1 - P(A υ B)
= 1 -
(ii) P
P(B) ; denote the probability that bus B will be late.
P(A) =
, P(B) = P
⇒ P(A ∩ B)(i) P(
∩ ) = 1 - P(A υ B)= 1 -
(ii) P
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