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Probability

I only need help with problems 1, 2, and 3. Please see the following website for the complete problems:http://www.isye.gatech.edu/people/faculty/Robert_Foley/classes/2027/hmwk3.pdf

1. Suppose that the sample space S = {1, 2, 3, ...}. Let pk = Pr({k}) for k 2 S. In each of the following
cases, compute c. (a) Suppose that pk = c(5/6)k for k 2 S; (b) Suppose that pk = c(5/6)k/(k)! for
k 2 S.
2. Suppose that the sample space is S = [0,1). Let Bt = [t,1) for any t  0. Suppose that Pr(Bt) =
ce−6t for t  0. Compute (a) c, (b) Pr(B2), and (c) Pr([1, 2)).
3. Suppose we are dealt 6 cards from a standard well-shuffled deck. What is the probability that there
are (a) a six card flush? (b) 4 of one kind and 2 of another? (c) two triples? (d) 3 pairs? (e) 2 pairs?
(f) 1 pair? (g) at least one pair? You may leave your answer in terms of
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Advnced probability problems are solved.

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