Discrete Math Two student council representatives are chosen

Discrete Math

Two student council representatives are chosen at random from a group of 7 girls and 3 boys. Let G denote the distribution over the number of girls chosen.

a. What is the range of G?

b. Give the distribution over the random variable G.

Solution

a)

G = {0,1,2}

b)

This will be a hypergeometric distirbution.

Note that the probability of x successes out of n trials is          
          
P(G) = C(N-G, n-G) C(K, G) / C(N, n)          
          
where          
N = population size =    10      
K = number of successes in the population =    7      
n = sample size =    2      
x = number of successes in the sample

Thus,

P(G) = C(10-G, 2-G) C(7, G) / C(10, 2)   [ANSWER]