On May 4, 1:43 pm, nage...@gmail.com wrote: > Hello, > > I am stuck with a probability problem. Here is the problem. Any help would be great. > > There are N samples each have probability of Pi (i=0......n-1) > > I want to find out probability of at least K of them occurs. Each is sampled only once. If probability of N events to be same it would have simpler. now since probability is different , not sure how to calculate this. Please also mention logic behind the calculations.
1. What's the result if K = 0? With that out of the way, assume K >= 1.
2. Let q (i, j) be the probability that exactly j of the first i samples occur, for 0 <= i <= n, 0 <= j < K. Let r (i) be the probability that K or more of the first samples occur.
Given that K > 0, what is q (0, 0), what is q (0, j) for 1 <= j < K, what is r (0)? Look at the definitions of q and r, and the result should be obvious.
For 1 <= i <= n: Since you know q (i-1, j) for 0 <= j < K, r (i-1), and p (i-1) which is the probability that the i-th sample occurs, how do you calculate q (i, 0), q (i, j) for 1 <= j < K, and r (i) ? There's a simple formula for each.
The desired result is r (n). Why?
3. For extra points: How do you reduce the number of calculations if K >= n / 2?