Question:
The probability of solving a problem in Mathematics by two students X and Y are \(\frac{1}{4}\) and \(\frac{1}{5}\) respectively. If both of them try to solve the problem independently, then the probability that the problem will be solved by exactly one of them is equal to :
The probability of solving a problem in Mathematics by two students X and Y are \(\frac{1}{4}\) and \(\frac{1}{5}\) respectively. If both of them try to solve the problem independently, then the probability that the problem will be solved by exactly one of them is equal to :
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Exactly one solves means X solves and Y fails, or X fails and Y solves; add the two products.
Updated On: Nov 12, 2026
- \(\frac{7}{20}\)
- \(\frac{1}{20}\)
- \(\frac{19}{20}\)
- \(\frac{12}{20}\)
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The Correct Option is A
Solution and Explanation
P(X) = \(\frac14\), P(Y) = \(\frac15\), independent events.
P(X solves, Y does not) \(=\frac14\times\frac45=\frac{4}{20}\).
P(Y solves, X does not) \(=\frac34\times\frac15=\frac{3}{20}\).
These are mutually exclusive, so P(exactly one) \(=\frac{4}{20}+\frac{3}{20}=\frac{7}{20}\).
Answer: (1) \(\frac{7}{20}\)
P(X solves, Y does not) \(=\frac14\times\frac45=\frac{4}{20}\).
P(Y solves, X does not) \(=\frac34\times\frac15=\frac{3}{20}\).
These are mutually exclusive, so P(exactly one) \(=\frac{4}{20}+\frac{3}{20}=\frac{7}{20}\).
Answer: (1) \(\frac{7}{20}\)
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