ProbabilityHard
Question
Let E and F be two independent events. The probability that exactly one of them occurs is 
and the probability of none of them occurring is 
. If P(T) denotes the probability of ocurrence of the event T, then
and the probability of none of them occurring is . If P(T) denotes the probability of ocurrence of the event T, thenOptions
A.P (E) = 4/5, P(F) = 3/5
B.P (E) = 1/5, P(F) = 2/5
C.P (E) = 2/5, P(F) = 1/5
D.P (E) = 3/5, P(F) = 4/5
Solution
Let P (E) = e and P (F) = f
⇒ e + f - 2ef =
......(1)
⇒ (1 - e) (1 - f) =
⇒ 1 - e - f + ef = ......(2)
From (1) and (2)
ef =
and e + f = 7/5.
Solving, we get
⇒ e + f - 2ef =
......(1)⇒ (1 - e) (1 - f) =
⇒ 1 - e - f + ef =
......(2)From (1) and (2)
ef =
and e + f = 7/5.Solving, we get
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