Find the probability.

Question

Two balls are drawn in succession without replacement from an urn containing 4 red balls and 3 black balls. Find the probability distribution of the number of black balls.

Answer 1

Outcome Probability

0 C(3,0)*C(4,2)/C(7,2) = 6/21

1 C(3,1)*C(4,1)/C(7,2) = 12/21

2 C(3,2)/*C(4,0)/C(7,2) = 3/21

where C(x,y) is combinations of x items taken y at a time

Answer 2

Start by finding the size of the sample space. Note that this is without replacement. 7 balls first pick x 6 balls second pick = 42.

Zero black: 4/7 * 3/6 = 12/42

Two black: 3/7 * 2/6 = 6/42

One black: 42-12-6 = 24/42