Question

A bag contains six marbles, of which four are red and two are blue. Suppose two marbles are chosen at random and X represents the number of red marbles in the sample.

Looking for the expected value of X.

Answer 1

Probability of 0 red = (2/6)(1/5) = 2/30
Probability of 1 red: 2*(4/6)(2/5) = 16/30
Probability of 2 red: (4/6)*(3/5) = 12/20

Expectation value = 0/30 + 16/30 + 24/30 = 4/3

Answer 2

0.933