There is a room filled with two types of urns.

Type X urns have 2 black marbles, 3 white.

Type Y urns have 4 black marbles, 1 white.

The two types of urn look identical, but 40% of them are Type X.

You pick an urn at random, and start drawing marbles at random without replacement.

a. If the first draw is black, what is the probability the urn is Type X?

b. If the first draw is black and the second draw is white, what is the probability the urn is Type X?

c. If the first draw is black and the second draw is white, what is the probability the third draw will be white?

8. There is a room filled with two types of urns. Type X urns have 2 black marbles, 3 white. Type Y urns have 4 black marbles, 1 white. The two types of urn look identical, but 40% of them are Type X. You pick an urn at random, and start drawing marbles at random without replacement. a. If the first draw is black, what is the probability the urn is Type X? b. If the first draw is black and the second draw is white, what is the probability the urn is Type X? c. If the first draw is black and the second draw is white, what is the probability the third draw will be white