Question

Urn 1 contains 2 white and 4 black balls and urn 2 contains 4 white and 4 black balls. If a ball is drawn at random from one of the two urns, what is the probability that it is a white ball?

Answer 1

Answer:
`(5)/(12)`

Explanation:

Given : Urn 1 contains 2 white and 4 black balls and urn 2 contains 4 white and 4 black balls.

Total balls in Urn 1 = 6

Total balls in Urn 2 = 8

Probability of drawing white ball from Urn 1 = P(W |Urn 1) =
`(2)/(6)`

Probability of drawing white ball from Urn 2 = P(W |Urn 2)=
`(4)/(8)`

Then probability that Urn1 is chosen =P(Urn 1)
`=(1)/(2)`

Similarly , P(Urn 2)
`=(1)/(2)`

By Law of total probability :

P(White)= P(W |Urn 1) x P(Urn 1) +P(W |Urn 2) x P(Urn 12)

`=(2)/(6)*(1)/(2)+(4)/(8)*(1)/(2)=(5)/(12)`

Hence, the probability that it is a white ball =
`(5)/(12)`