JEE Advance - Mathematics (1996 - No. 4)
For the three events $$A, B,$$ and $$C,P$$ (exactly one of the events $$A$$ or $$B$$ occurs) $$=P$$ (exactly one of the two events $$B$$ or $$C$$ occurs)$$=P$$ (exactly one of the events $$C$$ or $$A$$ occurs)$$=p$$ and $$P$$ (all the three events occur simultaneously) $$ = {p^2},$$ where $$0 < p < 1/2.$$ Then the probability of at least one of the three events $$A,B$$ and $$C$$ occurring is
$${{3p + 2{p^2}} \over 2}$$
$${{p + 3{p^2}} \over 4}$$
$${{p + 3{p^2}} \over 2}$$
$${{3p + 2{p^2}} \over 4}$$
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