Question:
In a question paper containing 10 questions, A can solve 70% of the questions and B can solve 50% of the questions. The probability, that none of A and B will be able to solve the question, selected at random from the paper, is :
In a question paper containing 10 questions, A can solve 70% of the questions and B can solve 50% of the questions. The probability, that none of A and B will be able to solve the question, selected at random from the paper, is :
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Treat the two events as independent; P(none) is the product of the probabilities of failing.
Updated On: Nov 12, 2026
- \( \frac{3}{10} \)
- \( \frac{3}{20} \)
- \( \frac{1}{5} \)
- \( \frac{2}{5} \)
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The Correct Option is B
Solution and Explanation
A solves a random question with probability \( \frac{70}{100} = \frac{7}{10} \), so A fails with probability \( \frac{3}{10} \).
B solves with probability \( \frac{1}{2} \), so B fails with probability \( \frac{1}{2} \).
Assuming the two events are independent, P(none can solve) = \( \frac{3}{10} \times \frac{1}{2} = \frac{3}{20} \).
Answer: (2) \( \frac{3}{20} \)
B solves with probability \( \frac{1}{2} \), so B fails with probability \( \frac{1}{2} \).
Assuming the two events are independent, P(none can solve) = \( \frac{3}{10} \times \frac{1}{2} = \frac{3}{20} \).
Answer: (2) \( \frac{3}{20} \)
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