Dan's Segment 5
1. There are five prime numbers between 2 and 12, they are 2, 3, 5, 7, and 11. So the probability of getting a prime on any given roll is 5/12. Calculating the probability of getting exactly 5 primes out of ten is a simple binomial calculation bin(5,10,5/12) which is about .214.
2. This is just a summation of binomial probabilities bin(N,i,1/2) where N goes from 500010000 to 500020000 and i = 1 billion. Wolfram alpha times out on this.
To Think About
1. This is basically the in class activity, which was done with LoriL, Rcardenas, and Travis. The full solution can be found on Travis' page. We could not write a program that did more than 10-12 at a time, but congratulations to Kai who figured out the most efficient way to do it and won $100.
2. I don't have mathematica, but I can say from experience that it probably generates a lot of other complicated conditional solutions depending on whether certain parameters are positive, negative, real, imaginary, etc.