Peter is giving marbles to some children at a carnival. He has 5 red marbles, 4 blue marbles, and 3 yellow marbles. If Peter selects a marble randomly without looking, what is the probability that he will give a blue marble to the first child and then a yellow marble to the second child?
4 over 12 plus 3 over 12 is equal to 7 over 12
4 over 12 plus 3 over 11 is equal to 80 over 132
4 over 12 multiplied by 3 over 12 is equal to 12 over 144
4 over 12 multiplied by 3 over 11 is equal to 12 over 132
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The initial number of marbles is 12, of which 4 are blue. Therefore the probability of selecting a blue marble first is 4/12. Having selected a blue marble, there is a total of 11 marbles remaining of which 3 are yellow. Therefore the probability of a yellow marble being selected second is 3/11.
The required probability is therefore given by