Let x be the number of successes observed in a sample of n = 7 items selected from a population of N= 14. Suppose that of the N = 14 items, M = 8 are considered "successes." Find the probability. (Round your answer to four decimal places.) the probability of observing at most two successes X

A group of people were asked if life exists elsewhere in the galaxy. 298 responded "Yes", and 359 responded "No". Find the probability that if a person is chosen at random, the person believes life exists elsewhere in the galaxy. Probability = 0.4534 x (Round to 4 decimal places)

There are 20 different pairs of shoes. Pick at random 10 shoes. Let X be the number of paired shoes, M be the number of shoes that are left-foot, N be the number of shoes that are right-foot.   (a)  Find the distribution of X. Show your problem-solving process (not just the final answer) with a few sentences of explanation and give the formula   (b)  Let Y = M – N. Give all possible values of Y. Find the distribution of Y. Show your problem-solving process (not just the final answer) with a few sentences of explanation and give the formula.   (c)  let Z = |Y|, compute E(X), Var(X), E(Z) and Var(Z). Show your problem-solving process (not just the answer), keep 2 decimal places for E(X) and E(Z), and use the approximate values for the calculations of Var(X) and Var(Z).