1)

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:

Option A

Explanation:

 concept involved

 it is a simple application of independent event,  us to solve a certain problem or any type of competition each event is independent of order.

   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 atleast one of them =1-(problem is not solved by all)

$\therefore$  P (problem is solved )=1-P

(Problem is solved)

   $=1-P(\overline{A)}.P(\overline{B)}.P(\overline{C)}.P(\overline{D)}$

     = $1-\left(\frac{1}{2}.\frac{1}{4}.\frac{3}{4}.\frac{7}{8}\right)$

    =$1-\frac{21}{256}=\frac{235}{256}$