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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 ______.
Options
`2/7`
`3/35`
`1/70`
`1/7`
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Solution
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`
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