Question

Two urns contain white balls and yellow balls. The first urn contains 3 white balls and 6 yellow balls and the second urn contains 7 white balls and 3 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white?

Answer 1

The first is a 1/3 chance, the second is a 3/10 chance.  Multiply them both, you get 3/30, or 1/10 chance.

Answer 2

The first urn has 9 balls and 3 of them are white.
The probability of pulling out a white one is 3/9 = 1/3 .

The second urn has 10 balls and 7 of them are white.
The probability of pulling out a white one is 7/10.

The probability of BOTH things happening is  (1/3) · (7/10) = 7/30 = 0.2333...