Question

Let E and F be two independent events. The probability that both E and F happen is `1/12` and the probability that neither E nor F happens is `1/2`, then a value of `(P(E))/(P(F))` is ______.

Options

• `4/3`

• `3/2`

• `1/3`

• `5/12`

Answer 1

Let E and F be two independent events. The probability that both E and F happen is `1/12` and the probability that neither E nor F happens is `1/2`, then a value of `(P(E))/(P(F))` is `bbunderline(4/3)`.

Explanation:

P(E∩F) = P(E). P(F) = `1/2`

P`(barE∩barF)=P(barE).P(barF) = 1/2`

(1 − P(E)) (1 − P(F)) = `1/2`

Let P(E) = x

P(F) = y

⇒ 1 − x − y + xy = `1/2` ⇒ 1 − x − y = `1/2 − 1/12 = 5/15`

⇒ x + y = `7/12 ⇒ x + 1/12x = 7/12`    [∴ x.y = `1/12`]

12x² − 7x + 1 = 0

12x2 − 4x − 3x + 1 = 0 = (4x − 1)(3x − 1) = 0

⇒ `x = 1/3, x = 1/4`

and y = `1/4, y = 1/3`

∴ `x/y = (1/3)/(1/4) = 4/3 or (1/4)/(1/3) = 3/4`