Complex NumbersHard

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

Options

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

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