A bag contains 10 green marbles and 4 yellow marbles. If two marbles are chosen at random, one at a time and without replacement, what is the probability of ge

Question

A bag contains 10 green marbles and 4 yellow marbles. If two marbles are chosen at random, one at a time and without replacement, what is the probability of getting two green marbles?

Answer 1

When you draw marbles without replacement, you are drawing the marbles and not putting them back.  This changes the composition of the marbles in the bag for the next draw.

 

Treat this marble like we are drawing one marble, then going back in for the second.  It doesn't effect the answer, but makes the problem easier to approach.

 

The probability of drawing the first green marble, P(green), is 10/14=5/7 since there are 10 green marbles out of the total 14.

 

For the probability of drawing the second green marble, we first assume we successfully drew the first green marble.  There  is little point of worrying about drawing a red marble first since we failed to get the outcome we wanted.  However, since we drew 1 green marble and didn't put it back, there is now one fewer green marbles and 1 fewer total marbles in the bag.

 

The probability of drawing the second green marble, P(2nd green),is 9/13 since there are now only 9 green marbles and only 13 total marbles.

 

When you perform two events in succession, you multiply their probabilities.

 

5/7 x 9/13 = 35/117