Question

We have two sealed boxes. In the first box we have 125 white and 75 black marbles. The second box contains 60 white and 90 black marbles. You pick a marble randomly from a box. For any given pick, the probability of picking from Box 1, P(B1) = 0.5. (a) What is the probability that the marble drawn is black? (b) The marble picked turns out to be black. What is the probability that it is picked out of Box 2?

Answer 1

(a)

P(Marble drawn is Black) = P(First Box is chosen & Marble drawn is Black) + P(Second Box is chosen & Marble drawn is Black)

                                        = (0.5 X 75/200)   + (0.5 X 90/150)

                                         = 0.1875 + 0.3

                                           = 0.4875

So,

Answer is:

0.4875

(b)

By Baye's Theorem:

P(Black/Box2) x P Box2) P(Box2/Black) = P(Black/Borl) x P(Borl) + P(Black/Bor2) X P(Box2)

0.5 x 90/150 (0.5 x 75/200) + (0.5 x 90/150)

103 0.1875 +0.3 0.3 0.4875 - = 0.6153

So,

Answer is:

0.6153