1. In a non-transparent bag there are 10 equally-weighted balls, each of them is marked by a number 3,5,4,4,7,7,7,1,9,9. Now we randomly pick 2 balls out of the bag and we note X as the smallest number among the 3 balls picked. The order is of no importance.(10 pt) a) What is the statistic distribution of X? b Compute E(X) and also ox. 2. Suppose that a factory products the same product using 4 different workshops A, B, C and D the producing capacity ratio of these workshops are A: B: C: D=1:1:2:4. The failure rates of product produced by these workshops are 20% for workshop A, 15% for workshop B, 30% for workshop C and 40% for workshop D. Now we randomly select a product produced by this factory. (10 pt) a) Using conditional probability theory, what is the probability that this product selected is a failure one ? b) If the product select is indeed a failure one, what is the probability that it's produced by workshop D? 3. There are 6 equally-weighted balls in a non-transparent bag, we know in advance that 2 of them are yellow balls, 1 of them is a white ball and 3 of them are red balls, now we randomly pick 2 balls out of the bag. (10 pt) a) Compute the probability of obtaining 2 red balls. b) Compute the probability of obtaining 1 yellow ball and 1 white ball. 4. Let us randomly select 4 different numbers from 0 to 9, use the combination equation to compute the probability that the sum of these 4 numbers selected less than 35. (10 pt)