Thanks for your help. I didn't realize that my teacher had said that the problems could use geometric distributions.

Here's my progress on each of the questions:

1. I used a binomcdf function with n=5 and p=1/12 ranging from 2 to 5 to account for combinations of 2, 3, 4, or all 5 people sharing the same sign. The multiplication by 12 is due to the possibility of any zodiac combination, and comes from nCr(12, 1), right? So I got about 70%, which seems somewhat high, but is still reasonable.

2. This problem seems really straightforward now.... I just performed a binomcdf function for n=100 and p=.3 from 0 to 25. This gave about 16%, which seems low but is probably reasonable.

3. The answer to this problem was really surprising.... When I found the expected value of the geometric distribution, I got 1. Does that mean that the ratio ends up being 1:1?

There's also a second part to the first question, which involves estimating the probability that at least one of the five people has the same zodiacal sign as yours. For this, would I do a binomcdf operation for n=5 and p=1/12 from 1 to 5 and

*not* multiply by 12? That gives about 35%, which seems to make sense.

Thanks so much.