If you have 1 red ball and 9 white balls in a bag, what is the probability of getting the red ball in 5 tries?

Question

If you have 1 red ball and 9 white balls in a bag, what is the probability of getting the red ball in 5 tries?

Answer 1

There are two ways to solve this problem.  The problem of getting the red ball in the first 5 tries equals the probability of getting the red ball in the last 5 tries; as there are 10 balls, then you have to select the ball in 10 tries.  Thus, the probability of selecting it in 5 tries is 1/2.

Solving this using combinatorics, P(1 red ball out of 5) = C(9,4)*C(1,1)/C(10,5)   -  the numerator is selecting 4 out of 9 white balls and one of 1 red balls; the numerator is selecting 5 of 10 balls.

C(9,4)*C(1,1)/C(10,5) = 9*8*7*6/4! * 1/(10*9*8*7*6/5!) = 9*8*7*6/4! * 1/(10*9*8*7*6/5*4!) = 5/10 = 1/2