JEE Advanced2013MathematicsProbabilityActual
Of the three independent events E 1 , E 2 and E 3 , the probability that only E 1 occurs is α , only E 2 occurs is β and only E 3 occurs is γ . Let the probability p that none of events E 1 , E 2 or E 3 occurs satisfy the equations α - 2 β p = α β and β - 3 γ p  =  2 β γ . All the given probabilities are assumed to lie in the interval 0, 1 . Then Probab
Correct answer
6
Step-by-step solution
Let x, y, z be probability of E 1 , E 2 , E 3 respectively ⇒ x 1 - y 1 - z = α ⇒ y 1 - x 1 - z = β ⇒ z 1 - x 1 - y = γ ⇒ 1 - x 1 - y 1 - z = P Putting in the given relation we get x = 2y and y = 3z ⇒ x = 6 z ⇒ x z = 6