probability

Question

There are 4 red 2 white and 4 blue marbles in an urn. Two marbles are selected at random without replacement. What is the probability that neither is red given that neither is white?

Answer 1

Given that neither of the two marbles selected is white, then what can they be?  They could be:

   R R

   R B

   B R

   B B

 

We might just as well have taken the white marbles out of the urn, since we won't even consider a selection of a white marble ("given that neither is white").

 

The probability of selecting a blue marble from the 4 blue and 4 red marbles is 4/8 (the ratio of success/total) = 1/2.

 

Now, with the first marble blue, the probability of selecting a blue marble for the second one (note: without replacement) is 3/7   (success/total).

 

This makes the probability of selecting two blue marbles (“neither is red” and “given that neither is white”) as:

    (1/2)(3/7) = 3/14.

Answer 2

If you are given that neither is white, then they must be blue or red. the odds that the first one drawn is blue is 1/2. the odds that the second is blue is 3/7. So the odds that both are blue is (1/2)(3/7) = 3/14