Question

Two events E and F are independent. If P(E) = 0.3, P(E ∪ F) = 0.5, then P(E|F) – P(F|E) equals ______.

पर्याय

• `2/7`

• `3/35`

• `1/70`

• `1/7`

Answer 1

Two events E and F are independent. If P(E) = 0.3, P(E ∪ F) = 0.5, then P(E|F) – P(F|E) equals `1/70`.

Explanation:

Given that: E and F are independent events such that

P(E) = 0.3 and P(E ∪ F) = 0.5

P(E ∪ F) = P(E) + P(F) – P(E ∩ F)

0.5 = 0.3 + P(F) – P(E).P(F)

⇒ 0.5 – 0.3 = P(F)[1 – P(E)]

⇒ 0.2 = P(F)(1 – 0.3)

⇒ 0.2 = P(F).(0.7)

∴ P(F) = `0.2/0.7 = 2/7`

Now `"P"("E"/"F") - "P"("F"/"E") = ("P"("E" ∩ "F"))/("P"("F")) - ("P"("E" ∩ "F"))/("P"("E"))`

= `("P"("E")."P"("F"))/("P"("F")) - ("P"("E")."P"("F"))/("P"("E"))`

= P(E) – P(F)

= `3/10 - 2/7`

= `1/70`