Probability

Question

A bag contains 8 red and 4 yellow marbles. Two marbles are chosen at random and not replaced. What is the probability that 1 marble will be yellow and 1 marble will be red?

1/32
2/33
16/33
1/8

 

Answer 1

Clearly, the first marble chose must be either red or yellow (assuming no other marbles in the bag). Drawing 2 without replacement yields 12*11 or 132 total combinations. So, compute the probability in each case that the 2nd is of the opposite color and combine the two together:

 

1st red: 8 possibilities with 4 chances 2nd yellow so 32 total 

1st yellow: 4 possibilities with 8 chances 2nd red so 32 total

Total probability 64/132 or 16/33