Question

From 22 potential women jurors and 25 potential men jurors, a jury of 12 is chosen at random. Let X be the number of women selected. Find the probability mass function of X.

Answer 1

Here we use the Hypergeometric distribution.

N = population size = # potential women jurors + # potential men jurors = 22 + 25 = 47

n = Number of draws = 12

M = element with a specific property in the population = # potential women juniors = 22

k = Hits for element with specific property = # of chosen at random = i

Where i = 0 , 1 , 2 , 3 , 4, 5 , 6 , 7,8 , 9 , 10 , 11 ,12

Probability mass function for Hypergeometric distribution

Where i = 0 , 1 , 2 , 3 , 4, 5 , 6 , 7,8 , 9 , 10 , 11 ,12

Final answer :-

Where i = 0 , 1 , 2 , 3 , 4, 5 , 6 , 7,8 , 9 , 10 , 11 ,12

I hope this will help you :)