28 You have a blue urn and a yellow urn the blude urn contai

#28 You have a blue urn and a yellow urn. the blude urn contains 3 blue balls and 1 yellow ball. the yellow urn contains 1 blue ball and 3 yellow balls. You choosea ball randomly from the yellow urn, replace the ball and choose a ball from the matching urn. Find the probability that the second is yellow is yellow?

#29 Continuing #28, find the probability that the 2 balls drawn are not the same color

Solution

28.

Let

B1 = 1st ball picked is blue
B2 = 2nd ball picked is blue
Y1 = 1st ball picked is yellow
Y2 = 2nd ball picked is yellow

Thus, by Bayes\' Rule,

P(Y2) = P(Y1) P(Y2|Y1) + P(B1) P(Y2|B1)

= (3/4)*(3/4) + (1/4)*(1/4)

= 0.625 [ANSWER]

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29.

P(not same) = P(Y1) P(B2|Y1) + P(B1) P(Y2|B1)

= (3/4)*(1/4) + (1/4)*(1/4)

= 0.25 [ANSWER]