1. You have k slots (of the same size) to drop n tokens into. How many ways
can you do this if the tokens are marked? Unmarked? (Hint: try with 3 tokens
and 7 slots first)
2. What is the probability of getting them all in the unique “winning” slot?
(Do you use the marked or unmarked count from #1 to compute this?)
3. What is the probability of getting at least two in the same slot (n≥2)?
4. What is the probability of getting at most one in each slot? At least one in
each slot, n≥k?
5. Suppose we let k approach in�finity, what happens in #4? Take a moment to
think about how slot size is important. It is certainly possible to �t infi�nitely
many slots into a �nite space. Do you have any insights if the slot sizes were
1/2 ft, 1/4 ft, 1/8 ft, 1/16 ft,....? (1=2+1=4+1=8+::: = 1) We need to assume
that the tokens are infi�nitely small. Clearly, there are in�finitely may possible
combinations. However, one is interested in determining the more probable
outcomes. Tip: Divide one bin into two and do the calculation. Then take the
right bin and divide it into two, calculate...etc.
It's our final review questions, and I really don't know how to solve these. Can anyone help me?
THX so much!!!
1 answer