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Q.
Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2},\frac{3}{4},\frac{1}{4},\frac{1}{8}$ Then,the probability that the problem is solved correctly by at least one of them, is
PLAN It is simple application of independent event, to solve a certain problem or any type of compitition each event in independent of other.
Formula used $P(A \cap B ) = P(A) . P(B)$, when $A$ and $B$ are independent events.
Probability that the problem is solved correctly by at least one of them $= 1 -$ (problem is not solved by all)
$\therefore P$ (problem is solved) $= 1 - P$ (problem is not solved)
$ =1-P(\overline{A}).P(\overline{B}).P(\overline{C}).P(\overline{D})$
$=1 - \bigg(\frac{1}{2},\frac{3}{4},\frac{1}{4},\frac{1}{8}\bigg)=1-\frac{21}{256}=\frac{235}{256}$