Among 10 applicants, 6 were women and 4 were men. The document finds the probability distribution of the number of women (X) and men (Y) selected in a random sample of 3 applicants. It gives the probability functions for X and Y as well as the relationships between them, with P(Y=i) equal to P(X=3-i) for i from 0 to 3.

1. Among 10 applicants for an open position, 6 are women and 4 are men. Suppose that three
applicants are randomly selected. Find the probability distribution for X, the number of female
among the findnal three.
a) give the probability function for X
b) defind Y, the number for male applicants among the final three, as a function X.
c) Find the probability function for Y
please show all work
Solution
P( X = 0 ) = 0.4^3
P( X = 1 ) = 3C1 * 0.4^2 * 0.6
P( X = 2 ) = 3C2 * 0.4 * 0.6^2
P( X = 3 ) = 0.6^3
P( Y = 0 ) = P( x = 3 )
P( Y = 1 ) = P( X = 2 )
P( Y = 2 ) = P( x = 1 )
P( Y = 3 ) = P( X = 0 )
P( Y = 0 ) = 0.6^3
P( Y = 1 ) = 3C2 * 0.4 * 0.6^2
P( Y = 2 ) = 3C1 * 0.4^2 * 0.6
P( Y = 3 ) = 0.4^3