A box with 5 white balls, and 4 balls from which four balls were selected. calculate:

Question

1. the probability of getting two white balls.
2. the probability of getting a white ball at most.
3. the probability of getting at least two blue balls.

Answer 1

Selecting 4 balls from a box with 5 white balls and 4 blue balls. 9 balls total

1. probability of getting two white balls

number of combinations of two white balls out of 5 * number of combination of 2 blue balls out of 4

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number of combinations of 4 balls out of 9

C(5,2) * C(4,2)/C(9,4) where C(x,y) = number of combination of y items out of x

2 probability of getting at most 1 white ball = probability of getting 0 white balls out of 4 + probability of getting 1 white ball out of 4:

C(5,0) * C(4,4)/C(9,4) + C(5,1)*C(4,3)/C(9,4)

3. Probability of getting at least 3 blue balls = probability of getting 3 blue balls out of 4 + probability of getting 4 blue balls out of 4:

C(5,1)*C(4,3)/C(9,4) + C(5,0)*C(4,4)/C(9,4)