Question

Urn "A" contains 5 white balls and 4 black balls, whereas urn B contains 3 white balls and 5 black balls. A ball is drawn at random from urn "B" and placed in urn "A". A ball is then drawn from urn "A". It happens to be black. What is the probability that the ball transferred was black?

Answer 1

We have given that,

Urn "A" contains 5 white & 4 black balls.The total number of balls in Urn "A" are 9.

Urn "B" contains 3 white & 5 black balls. The total number of balls in Urn "B" are 8.

A ball is drawn from Urn "B" is

⁸C₁=8 combinations

& placed in Urn "A". Then a ball is drawn from Urn "A" is black.

But, we have find probability that a ball drawn from Urn "B" which is placed in Urn "A" is black denoted by p(C).

C: The ball transferred from Urn "B" to Urn "A" is black.

p(C)= ⁵C₁/⁸C₁

p(C)=5/8=0.625.