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
The students work independently, and the problem is solved if at least one of them solves it. The complement is that none of them solves it:
\( \displaystyle P(\text{none}) = \left(1 - \frac{1}{2}\right)\left(1 - \frac{1}{3}\right)\left(1 - \frac{1}{4}\right) \)
\( \displaystyle = \frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4} = \frac{1}{4} \)
\( \displaystyle P(\text{solved}) = 1 - \frac{1}{4} = \frac{3}{4} \)