A problem in mathematics is given to three students whose chances of solving it are 1/2, 1/3, 1/4 respectively. The probability that the problem is solved is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 3/4 **
Let the probabilities of solving the problem be:
$P_{1}=\frac{1}{2},\; P_{2}=\frac{1}{3},\; P_{3}=\frac{1}{4}$
Probability that none of them solves:
$\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)$
$=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}$
$=\frac{1}{4}$
Therefore probability that at least one solves:
$1-\frac{1}{4}=\frac{3}{4}$
The required probability is $\frac{3}{4}$.