Question

1. An urn contains 4 red balls, 3 black balls and 2 green balls. We draw two balls at random (without replacement). If at least one of the two balls is red, we draw one more ball and stop. Otherwise, we draw two more balls without replacement. (i) Compute the probability that the last bal is red (NOTE that for this entire question, your notation is at least as impor tant as your final numerical answer. So, for example, do not just write down a couple of numbers in a tree diagram. Instead define your events properly, write out the probabilities in terms of the events and show your reasoning/calculations clearly.) (ii) If we know that the first selected ba is black, what is the probability that the last bal is red? (ii) If we know that the last ball is red, what is the probability that the first ball is black?

Answer 1

iven Red balls : Total 스 9 n one of the wo l occos is) = 0, 62962a6