Probability question (2)

Question

Three marbles are randomly drawn from a bag containing six white marbles balls and four black marbles.

Part a) What is the probability of there being: 3 white marbles. Round your answer to the nearest two decimals: 0.00

Part b) What is the probability of there being: 1 white marble and 2 black marbles. Round your answer to the nearest two decimals: 0.00

Answer 1

We can either use combinatorics or the hypergeometric distribution to solve this problem.

We have 10 balls, 6 white and 4 white

a)P(3 white of 3) =

C(6,3)C(4,0)/C(10,3) = 20*1/120 = 1/6

b)

P(1 white and 2 black) =

C(6,1)C(4,2)/C(10,3) = 6 * 6/120 = 3/10

Using hypergeometrics, if we view white as a success, in Excel,

=hypgeom.dist(success in sample, size of sample, success in population, size of population, 0 = exact) =

a) hypgeom.dist(3,3,6,10,0) = 1/6

b) hypgeom.dist(1,3,6,10,0) = 3/10