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# Probability

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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&#8722;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
&#65533;&#65533;n
k

.

https://brainmass.com/math/probability/probability-sample-space-functions-7753

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1. Solution. Let us denote being head by H and being the number by N respectively when flipping one coin. We know that rolling one die corresponds to possible six results:1,2,3,4,5 or 6. So
a) A reasonable sample space S for this experiment is as follows.

S={{H,1},{H,2},{H,3},{H,4},{H,5},{H,6},{N,1},{N,2},{N,3},{N,4},{N,5},{N,6}}

Note: one sample point in S, say {H,1} means the result of the experiment is with the head of coin up and roll a 1.

b) {H,1} means the result of the experiment is with the head of coin up and roll a 1;
{H,2} means the result of the experiment is with the head of coin up and roll a 2;
{H,3} means the result of the experiment is with the head of coin up and roll a 3;
{H,4} means the result of the experiment is with the head of coin up and roll a 4;
{H,5} means the result of the experiment is with the head of coin up and roll a ...

#### Solution Summary

The probability sample space functions are examined. The standard well-shuffled deck is determined.

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