Suppose 3 balls are drawn at random from a box containing 8red,3white and 9blue balls,combinatorial analysis can be employed to determine the probability that,for instance,all balls drawn are red.determine that: I. At least one is white.

Question

Suppose 3 balls are drawn at random from a box containing 8red,3white and 9blue balls,combinatorial analysis can be employed to determine the probability that,for instance,all balls drawn are red.determine that: I. At least one is white.

II.one of each color is drawn.

Answer 1

8 red

3 white
9 blue
total = 20

at least one is white
---- exclude case of all non-white

prob(that 3 of 19 are all non-white)
= C(17,3) x C(3,0)/C(20,3)
= 680/1140
= 34/57

prob(at least one white)
= 1 - 34/57
= 23/57

one of each colour
= C(8,1) x C(3,1) x C(9,1)/c(20,3)
= 216/1140
= 18/95