Solving a Probability Problem with Bayes Theorem

[ENgez]

Homework Statement

you have a sack with 5 red balls, 5 black balls and 5 white balls. you take them out one at a time without returning until the sack is empty. what is the probability the last ball you took out is red given that the first ball taken out is not white.

Homework Equations

it should be solvable using the bayes theorom, the definition of conditioned probability, and the complete probability formula.

The Attempt at a Solution

i tried playing around with different events and using the formulas above but no luck... the main problem is that the probability tree is huge. i was hoping i can get a push in the right direction.

thanks.

 

[tiny-tim]

Hi ENgez!

You have a sack with 5 red balls, 4 black balls and 5 white balls. You take them out one at a time without returning until the sack is empty. what is the probability the last ball you took out is red?