Q10 of 39 Page 1

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

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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