The probabilities of solving a problem by students A, B and C independently are $\frac{1}{2}, \frac{1}{3}$, and $\frac{1}{4}$ respectively. If they start solving the given problem. independently, then the probability that atleast two of them will solve the problem successfully, is equal to
Answer & explanation
Correct answer: option 3
Probability that A and B can solve but ‘C’ is unable to solve
$=\frac{1}{2} . \frac{1}{3} . \frac{3}{4}=\frac{1}{8}$
Probability that A and C can solve but ‘B’ is unable to solve
$=\frac{1}{2} . \frac{2}{3} . \frac{1}{4}=\frac{1}{12}$
Probability that B and C can solve but ‘A’ is unable to solve
$=\frac{1}{2} . \frac{1}{3} . \frac{1}{4}=\frac{1}{24}$
Probability that all of them can solve the problem
$=\frac{1}{2} . \frac{1}{3} . \frac{1}{4}=\frac{1}{24}$
Thus required probability that atleast two of them can solve the problem
= $\frac{7}{24}$