Question

Consider selecting one ball at a time from a box which contains 8 red, 5 yellow and 2 blue balls. What is the probability that the first and second balls are yellow? Show all work.
(a) Assume the ball selection is without replacement.
(b) Assume the ball selection is with replacement.

Answer 1

Part a

Solution:

We are given

Total number of balls = 8+5+2 = 15

Total number of yellow balls = 5

P(First ball is yellow) = 5/15

P(Second ball is yellow) = 4/14

(Due to without replacement)

P(First and second ball is yellow) = (5/15)*(4/14) = 0.095238095

Required probability = 0.095238095

Part b

Solution:

We are given

Total number of balls = 8+5+2 = 15

Total number of yellow balls = 5

P(First ball is yellow) = 5/15

P(Second ball is yellow) = 5/15

(Due to with replacement)

P(First and second ball is yellow) = (5/15)*(5/15) = 0.111111111

Required probability = 0.111111111