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 = αβ and ( β – 3 γ ) p = 2 βγ . All the given probabilities are assumed to lie in the interval (0, 1).
Then 
=
Text Solution
Verified by Experts6
(6)
Sol. 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 = 6z ⇒ 
= 6
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