1.We have two urns. The first urn contains three balls labeled 1, 2 and 3, respe

Question

1.We have two urns. The first urn contains three balls labeled 1, 2 and 3, respectively. The second urn contains four balls labeled 2, 3, 4 and 5, respectively. We choose one of the urns randomly, so that the probability of choosing the first one is 1/5. Then we sample one ball (uniformly at random) from the chosen urn. Suppose the ball 3 was chosen. What is the probability that it came from the second urn?

2.I have a bag with 3 fair dice. One is 4-sided, one is 6-sided, and one is 12-sided. I reach into the bag, pick one die at random and roll it twice. The first roll is a 3 and the second roll is a 4. What is the probability that I pulled out the 6-sided die?

3.Suppose events A, B, C, D are mutually independent. Show that events AB and CD are independent. Justify each step from the definition of mutual independence.

Explanation / Answer

P( first urn)=1/5 P(2nd urn=4/5)

P( Ball 3/ Second urn) = 4/5*1/4/[4/5*1/4+1/3*1/5]=3/4=0.75

Please post the other questions individually

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