Question

Suppose X has a hypergeometric distribution with n=100, n = 4, K = 20. Determine P (X = 1).

Answer 1

To determine P(X = 1) in the given hypergeometric distribution, calculate the probability of selecting 1 success from the group of interest and 99 failures from the rest of the population using the formula and factorial values.

Step-by-step explanation:

To determine P(X = 1) in the given hypergeometric distribution with n = 100, K = 20:

1. Calculate the probability of selecting 1 success from the group of interest (20) and 99 failures from the rest of the population (80) using the formula:

P(X = 1) = (20 choose 1) * (80 choose 99) / (100 choose 100)

1. Substitute the binomial coefficient values into the formula:

P(X = 1) = (20! / (1!(20-1)!)) * (80! / (99!(80-99)!)) / (100! / (100!(100-100)!))

1. Calculate the final result using the factorial values:

P(X = 1) = (20 * 80!) / (1! * (20-1)! * 99! * 100! / (100!(100-100)!))

Therefore, P(X = 1) is equal to the calculated value in the final step.