00:01
To solve this problem, we can use the hypergeometric distribution.
00:06
So in this case, we have a population of 25 animals, out of which 5 are tagged.
00:11
So we want to find the probability of selecting no more than 2 tagged animals in a sample of 10 without replacement.
00:19
So the probability mass function is given by p x equals x, which equals c times k and x times c of n minus k n minus x divided by c times n and n, where n is the population size, k is the number of success states in the population, n is the number of draws, x is the number of observed successes, c a b represents the binomial coefficient.
01:01
Now let's calculate the probability for each case, 0, 1, and 2 tagged animals and then sum them up.
01:10
So first we have p of x is less than or equal to 2, which equals p of x equals 0 plus p of x equals 1 plus p of x equals 2.
01:29
So for p of x equals 0, we have c 5 0 times c 25 minus 510 minus 0 divided by c 25 10...