Suppose we have a group of 100 students where 20 are seniors

Suppose we have a group of 100 students where 20 are seniors. Take a random sample of 7 students without replacement. Let X represents the number of seniors in the sample. Find P(X = 3).

Solution

Suppose we have a group of 100 students where 20 are seniors. Take a random sample of 7 students without replacement. Let X represents the number of seniors in the sample. Find P(X = 3).

The hyper geometric distribution is used to calculate probabilities when sampling without replacement

P(X=x) = (_N1C_x) (_N-N1C_n-x) (_NC_n)^-1   

P(X = 3) = 0.1126