In a bag are only red and white marbles....

Question

In a bag are only red and white marbles. The probability of choosing a red marble is 3/5. The Probability of choosing 2 red marbles is without replacement is 3/10. How many white marbles are in the bag?

Answer 1

If we let r and w be original # of red & white marbles,

P(red) = r/(r+w) = 3/5 which implies that r+w = (5/3)r ... Eq. One

 

On second draw w/o replacement, P(red,red) = (3/5)(r-1)/(r+w-1) = 3/10.

Therefore (r-1)/(r+w-1) = 1/2 ...  Eq. Two.

By cross-multiplying we have 2r-2 = r+w-1 and into this we substitute from Eq. One for the expression (r+w):

2r - 2 = (5/3)r - 1

(1/3)r = 3 so r = 9.

 

This leads to w = 6.