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)

$\frac{235}{256}$

Answer 2

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