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A question is given to three students A, B and C whose
chances of solving it are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. What is the probability that the question will be solved?
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chances of solving it are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. What is the probability that the question will be solved?
Solution:
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Verified Answer
The correct answer is:
$\frac{3}{4}$
Required probability $=1-\left(\mathrm{P}^{\prime}(\mathrm{A}) . \mathrm{P}^{\prime}(\mathrm{B}) . \mathrm{P}^{\prime}(\mathrm{C})\right)$
$=1-\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)$
$=\left(1-\frac{1}{2} \times \frac{2}{3} \times \frac{3}{4}\right)$
$=1-\frac{1}{4}=\frac{3}{4}$
$=1-\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)$
$=\left(1-\frac{1}{2} \times \frac{2}{3} \times \frac{3}{4}\right)$
$=1-\frac{1}{4}=\frac{3}{4}$
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