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 atleast one of them, is ?

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

Answer 1

The correct option is A $\frac{235}{256}$

It is simple application of independent events condition.
Formula used :
$P(A\cap B)=P\left(A\right).P\left(B\right)$, when A and B are independent events.
Here, Probability that the problem is solved correctly by atleast one of them = 1- (Problem is not solved by any of them)
$\therefore$ P (problem is solved)
$=1-P\left(\overline{A}\right).P\left(\overline{B}\right).P\left(\overline{C}\right).P\left(\overline{D}\right)=1-(\frac{1}{2}.\frac{1}{4}.\frac{3}{4}.\frac{7}{8})=1-\frac{21}{256}=\frac{235}{256}$