ProbabilityHard
Question
A and B are two independent events. The probability that A and B happen simultaneously is 
and neither A nor B happens is 
, then which of the following are true :
and neither A nor B happens is , then which of the following are true :Options
A.P(A) = 1/3, P(B) = 1/4
B.P(A) = 1/2, P(B) = 1/6
C.P(A) = 1/4, P(B) = 1/3
D.P(A) = 1/6, P(B) = 1/2
Solution
P(A ∩ B) = P(A) . P(B) = 
......(i)
= P
. P
= 
⇒ (1 - P(A)) (1 - P(B)) =
⇒ 1 - P(A) – P(B) + P(A) P(B) =
⇒ 1 - P(A) – P(B) +
= 
⇒ P(A) + P(B) =
.......(ii)
Solving (i) and (ii) gives P(A) =
Accordingly, P(B) =
......(i) = P . P = ⇒ (1 - P(A)) (1 - P(B)) =
⇒ 1 - P(A) – P(B) + P(A) P(B) =
⇒ 1 - P(A) – P(B) +
= ⇒ P(A) + P(B) =
.......(ii)Solving (i) and (ii) gives P(A) =
Accordingly, P(B) =
Create a free account to view solution
View Solution FreeMore Probability Questions
A fair coin is tossed 9 times the probability that at least 5 consecutive heads occurs is...A & B throw with one dice for a stake of Rs. 99/- which is to be won by the player who first throws 4. If A has the firs...A local post office is to send M telegrams which are distributed at random over N communication channels, (N > M). Each ...One of the two events must occur. If the chance of one is 2/3 of the other, then odds in favour of the other are-...A 9 digit number using the digits 1, 2, 3, 4, 5, 6, 7, 8 & 9 is written randomly without repetetion. The probability tha...