Question

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

• A. $\frac{235}{256}$
• B. $\frac{21}{256}$
• C. $\frac{3}{256}$
• D. $\frac{253}{256}$

Answer 1

Answer: (A)

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)
$=1-P(\overline{A}).P(\overline{B}).P(\overline{C}).P(\overline{D})$
$=1-(\frac{1}{2},\frac{3}{4},\frac{1}{4},\frac{1}{8})=1-\frac{21}{256}=\frac{235}{256}$