NDA 2 2024 Maths, question 114

Topic: Probability

Q114

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?

(a) $11/20$
(b) $7/12$ Correct answer
(c) $3/5$
(d) $1$

Solution.

Answer: (b) $7/12$

A white or black transfer from A each has probability 1/2.
After a white transfer B has 4 white out of 6; after a black transfer it has 3 out of 6.
Total probability of white is (1/2)(4/6)+(1/2)(3/6)=7/12.