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 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. 1/11
b. 3/10
c. 2/33
d. 1/9

Answer 1

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

Answer: Choice A) 1/11