Question

Urn A has 8 Red balls and 5 Green balls while Urn B has 1 Red ball and 3 Green balls.
A fair die is tossed. If a “5” or a “6” are rolled, a ball is drawn from Urn A. Otherwise, a ball is drawn from Urn B.
(a) Determine the conditional probability that the chosen ball is Red given that Urn A is selected?
(b) Determine the conditional probability that the chosen ball is Red and Urn B is selected?
(c) Determine the probability that the chosen ball is Red.

Answer 1

Note: The language of part “b” is not correct. There can be two things:

1) Determine the conditional probability that the chosen ball is Red given that Urn B is selected?

Ans: P(R|B) = 1/4 = 0.25    or

2) Determine the probability that the chosen ball is Red and Urn B is selected?

Ans: P(R and B) = (1/4)•(2/3) = 1/6

Reason, “conditional probability” comes with “given that”. In part b, either there will be “given that” in place of and. Or another chance, there will be “probability” in place of “conditional probability”.

Let me know if you need any further explanation. Thank you