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# Probability: Sample Spaces

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Please see http://www.isye.gatech.edu/people/faculty/Robert_Foley/classes/2027/hmwk2.pdf for the fully formatted problems.

Probability: This is where the homework 2 is found. I couldn't attach the files for some odd reason. But I ONLY NEED HELP ON PROBLEM # 2, 3, AND 4.

2. Let the sample space be S = {1, 2, 3, 4, 5}. Define Ak = {k} and Bk = {k, k+1, . . . , 5} for k = 1, . . . , 5.
Suppose Pr(Ak) = ck for k 2 S. Determine the value of c. Compute Pr(Ak) and Pr(Bk) for k 2 S.
3. Let the sample space be S = {0, 1, 2, . . . }. Define Ak = {k} and Bk = {s 2 S|s  k} for k 2 S.
Suppose Pr(Ak) = c6k/k! for k 2 S. Determine the value of c. Compute Pr(A0) and Pr(B1).
4. Let the sample space S be the (strictly) positive integers. Let Ak = {k} for k 2 S. Suppose Pr(Ak) =
c(1/6)k for k 2 S. Determine c and Pr(A1).

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2. Solution. Since Ak={k}, k=1,3,5,6 and Pr(Ak)=ck. We therefore have
Pr(A1)=c, Pr(A3)=3c, Pr(A5)=5c and Pr(A6)=6c. Thus,
Pr(A1)+Pr(A3)+Pr(A5)+Pr(A6)=c+3c+5c+6c=14c .........(1)
Since the sample space S={1,3,5,6}=A1 A3 A5 A6, (1) will be
...

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Probability problems are solved. The solution is detailed and well presented.

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