a bag contains 56 marbles. each marble is either red, green, or yellow. a marble is randomly removed from the bag and then retur
ned to the bag. the probability that this marble is red is 5/8. the probability that this marble is green is 1/7. how many yellow marbles are in the bag?
The first time I solved this problem, I did it in a way that I had to mess with changing fractions to common denominators and all that. Suddenly, however, the clean and easy way to do it dawned on me. Here it is:
-- There are 56 marble in the bag.
-- The probability of pulling a red marble is 5/8, so 5/8 of the 56 marbles must be red. 5/8 of 56 = 35 red marbles.
-- The probability of pulling a green marble is 1/7, so 1/7 of the 56 marbles must be green. 1/7 of 56 = 8 green marbles.
-- The red and green marbles make up (35 + 8) = 43 of the 56 marbles in the bag.
-- The rest of them are yellow. There are (56 - 43) = 13 yellow marbles in the bag.
-- The probability of pulling a yellow marble is 13/56 . (about 23.2%)
No messy fractions at all ! That's the way I like it !
