CUET · MATHS · PYQ PAPER 2025
Bag A contains 2 unbiased and 3 biased coins whereas Bag B contains 3 unbiased and 2 biased coins. A bag is selected at random and 2 coins are taken out simultaneously. The probailty, that both coins are unbiased is :
- A \(\frac{1}{5}\)
- B \(\frac{1}{10}\)
- C \(\frac{2}{5}\)
- D \(\frac{3}{10}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{5}\)
Step-by-step Solution
Detailed explanation
\(P(\text{2 unbiased}) = P(\text{Bag A})P(\text{2U | A}) + P(\text{Bag B})P(\text{2U | B})\) \(= \frac{1}{2} \cdot \frac{\binom{2}{2}}{\binom{5}{2}} + \frac{1}{2} \cdot \frac{\binom{3}{2}}{\binom{5}{2}}\) \(= \frac{1}{2} \cdot \frac{1}{10} + \frac{1}{2} \cdot \frac{3}{10}\)…
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