Two urns contain white balls and yellow balls. The first urn contains 3 white balls and 6 yellow balls and the second urn contains 3 white balls and 8 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white?
A = event that the ball drawn from urn #1 is white B = event that the ball drawn from urn #2 is white
P(A) = probability of event A P(A) = (number of white in urn #1)/(number total in urn #1) P(A) = 3/(3+6) P(A) = 3/9 P(A) = 1/3
P(B) = probability of event B P(B) = (number of white in urn #2)/(number total in urn #2) P(B) = 3/(3+8) P(B) = 3/11
Because A and B are independent events, we can multiply the probabilities P(A and B) = P(A)*P(B) P(A and B) = (1/3)*(3/11) P(A and B) = (1*3)/(3*11) P(A and B) = 1/11
