Please help me with the probability?

Question

An urn contains 3 red balls and 6 white balls. Draw 3 balls randomly one after another without replacement. Find the probability that the second and third balls are the same color. Show work

Answer 1

Assuming that the first ball is a different color from the second and third balls...

 

there are two choices

 

white, red, red or red, white, white

 

(6/9)(3/8)(2/7) + (3/9)(6/8)(5/7)=

(2/3)(3/8)(2/7) + (1/3)(3/4)(5/7)=

simplify now or after

12/168 + 15/84=

1/14 + 5/28=

2/28 + 5/28=

7/28=

1/4