Can you help by working this out for me please

Question

2. A bag contains 24 pieces of candy, of which 12 are peppermints and 12 are butterscotch. Let X be the number of peppermints in a sample of 5 pieces of candy selected at random and without replacement from the bag. Find the following:

1. Pr(X=2)

2. Pr(X≤2)

3.E(X),σ= √VarX

Answer 1

Since you are sampling without replacement, you would use the hyper-geometric probability formula to solve this problem.

N = number of items in the population (24)

k = number of items in the population that are classified as a success (12)

n = number of items in the sample (5)

x = number of items in the sample that are classified as successes

C C

k x N-k n-x

----------------------

C

N n

For 1, x = 2

For 2, compute probability for x = 0, 1 and 2 and add together

Mean of hyper-geometric distribution is n*K/N

Variance is n*k*(N-k)*(N-n)/[N^2 * (N-1)]