MATH 301/601, Test 1, February 8, 20061.From the integers 1,...,10, three numbers are chosen at random withoutreplacement and disregarding the order.(a)In how many ways can this be done?(b)What is the probability that the smallest number is 4?(c)Do (a) and (b) with 10 replaced by an integernand 4 replaced by anintegerk(wheren≥3 andk≤n-2)2.Consider two urns such that urn I has two black balls and urn II has oneblack ball and one white ball. You choose an urn at random and then pick aball from this urn.(a)If the ball is black, what is the probability that you chose urn I?(b)If you draw twice with replacement from the chosen urn and get twoblack balls, what is the probability that you chose urn I?(c)If you drawjtimes with replacement from the chosen urn and only getblack balls, what is the probability that you chose urn I?3.LetAandBbe events. Are the following statements true or false?
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