probability on marble

Question

A bag contains 5 marble. One marble is black an the others are yellow. Samantha will randomly remove one marble at a time. What is the probability she will take out the black marble on her second pick?

Answer 1

There is only 1 way to take out the black marble on the second pick, and that is to take out a yellow marble on the first pick and the black marble on the second pick.  

 

P(Y on 1st pick) = 4/5

P(B on 2nd pick) = 1/4  since there are now only 4 marbles left 

 

The probability that both of these things happen is the product (4/5)*(1/4) = 4/20 = 1/5 = 0.2 

 

There's another way of looking at this problem, which is if you keep drawing until all 5 marbles are picked then you must have picked the black marble at some point, in the 1st, 2nd, 3rd, 4th or 5th pick.  If you are removing the marbles randomly then the black marble is equally likely to be removed on any of these 5 picks, so the probability that the black marble is taken out on any pick is 1/5.  That is, P(B on 1st pick) = P(B on 2nd pick) = P(B on 3rd pick) = P(B on 4th pick) = P(B on 5th pick) = 1/5.