Of the three independent events E 1 , E 2 , and E 3 , the probability that only E 1 occurs is 
, only E 2 occurs is 
and only E 3 occurs is 
. Let the probability p that none of events E 1 , E 2 or E 3 occurs satisfy the equations 
and 
. All the given probabilities are assumed to lie in the interval (0, 1).
Then 
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Text Solution
Verified by Experts6
(6)
Let P (E 1 ) = x, P (E 2 ) = y and P (E 3 ) = z
then (1 - x) (1 - y) (1 - z) = p
x (1 - y) (1 - z) = 
(1 - x) y(1 - z) = 
(1 - x) (1 - y) (1 - z) = 
so 
similarly z= 
so 
also given 
Substituting back 
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