MHT CET · Maths · Probability
A problem in statistics is given to three students \(\mathrm{P}, \mathrm{Q}\) and \(\mathrm{R}\). Their chances of solving
the problem are \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\) respectively. If all of them try independently, then the
probability that the problem is solved, is
- A \(\frac{2}{3}\)
- B \(\frac{1}{2}\)
- C \(\frac{3}{4}\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{3}{4}\)
Step-by-step Solution
Detailed explanation
(B)
P (Problem will be solved)
\(=1-\mathrm{P}\) (Problem will not be solved by \(\mathrm{P}, \mathrm{Q} \& \mathrm{R}\) )
\(=1-\left[\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\right]\) \(=1-\left(\frac{1}{2} \times \frac{2}{3} \times \frac{3}{4}\right)=1-\frac{1}{4}=\frac{3}{4}\)
P (Problem will be solved)
\(=1-\mathrm{P}\) (Problem will not be solved by \(\mathrm{P}, \mathrm{Q} \& \mathrm{R}\) )
\(=1-\left[\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\right]\) \(=1-\left(\frac{1}{2} \times \frac{2}{3} \times \frac{3}{4}\right)=1-\frac{1}{4}=\frac{3}{4}\)
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