Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?

Question

Question

This question was previously asked in

NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)

Answer 1

Explanation:

Given:

Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls.

⇒ E1 = One white ball transferred from A to B; then urn A contains white = 1 and b = 2 and urn B contains white = 4 and black = 2

⇒ E2 = One black ball transferred from A to B. Then urn A contains white = 2 and black = 1 and urn B contains white = 3 and black = 3

⇒ F = One white ball is drawn from urn B

⇒ \(P(F) =P(E_1). P(\frac{F}{E_1})+ P(E_2).P(\frac{F}{E_2})\)

= \(\frac{2}{4}\times\frac{4}{6}+\frac{2}{4}\times\frac{3}{6} = \frac{7}{12}\)

∴ Option (b) is correct.

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