1). A corporation is sampling without replacement for n = 3 firms to determine the one from which to purchase certain supplies. The sample is to be selected from a pool of six firms, of which four are local and two are not local. Let Y denote the number of nonlocal firms among the three selected.
(a) Find P (Y = 1).
(b) Find P (Y >= 1).
(c) Find P (Y <= 1).
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2).The probability that a married man watches a certain television show is 0.4 and the probability that a married woman watches the show is 0.5. The probability that a man watches the show, given that his wife does, is 0.7. Find the probability that
(a) a married couple watches the show;
(b) at least 1 person of a married couple will watch the show.
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3).The probability that an automobile being filled with gasoline will also need an oil change is 0.25; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and filter need changing is 0.14. If the oil had to be changed, what is the probability that a new oil filter is needed?