[jenng]

urn 1 contains 3 red balls and 3 black balls. Urn 2 contains 2 red balls and 2 black balls. Urn 3 contains 3 red balls and 3 black balls. If an urn is selected at random and a ball is drawn, find the probability that it will be red
p(red)=

[ebaines]

Here's a hint: P(red) = P((urn 1 & red) or (urn 2 & red) or (urn 3 & red)) = P(urn 1 & red) + P(urn 2 & red) + P(urn 3 & red)

where P(urn N & color) is the probability of selecting urn N and then choosing a ball of color COLOR from that urn. For example: P(urn 1 & red) = 1/3 x 3/6, because (a) there is a 1/3 chance of selecting urn 1 and (b) three out of the 6 balls in urn 1 are red. You can complete the calculations for the other two urns and sum up the probabilities to get P(red).