Q. 10

# Prove that if E and F are independent events, then the events E and F are also independent.

Answer :

Given; E and F are independent events

⇒ P(E⋂F) = P(E).P(F)

⇒ P(E⋂F’) = P(E) − P(E⋂F)

= P(E) − P(E).P(F)

= P(E) [1− P(F)]

= P(E).P(F’)

∵ P(E⋂F’) = P(E).P(F’)

∴ E and F’ are independent.

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If A and B are two independent events such that P(A’ ∩ B) = 2/15 and P(A ∩ B’) = 1/6 then find P(A) and P(B).

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