EECS 501__________________________PROBLEM SET #2__________________________Fall 2001

**ASSIGNED:** Sept. 14, 2001. Read Stark and Woods pp. 13-36 and 52-60.

**DUE DATE:** Sept. 21, 2001. THIS WEEK: Conditional probability and combinatorics

- Stark and Woods #1.24. A "story" problem (actually very simple).
- Stark and Woods #1.25. A simple conditional probability problem.
- Stark and Woods #1.35. Also show both answers reduce to mp when p < < 1 and N=1.
- Stark and Woods #1.15. Do this in
*sample space*--don't get fancy!
- Stark and Woods #1.16. A simple Bayes's rule problem.

- From the A.W. Drake book (see what I mean about not missing it?):
- Die A has 5 olive faces and 1 lavender face;
- Die B has 3 olive faces and 3 lavender faces.
- However awful their face colors may be, both dice are known to be fair.
- A fair coin is flipped once. Then:
- If it falls heads, throw die A n+1 times;
- If it falls tails, throw die B n+1 times.

- Compute Pr[nth throw of whichever die is used is olive].
- Compute Pr[nth AND (n+1)st throws of the die are both olive].
- Given that the first n throws of the die all resulted in olive,
compute the conditional

probability that the (n+1)st throw will result in olive.
Interpret your result for large n.

- A combinatorical interpretation of a mathematical identity:
- k balls are selected at random from a box containing n white balls
and m black balls.

Compute Pr[r of the k balls are white].
- Use the result of (a) to compute the sum:

Q: What do the Detroit Lions and evangelist Billy Graham have in common?

A: Both can make 80,000 people scream "Jesus Christ!" simultaneously.