Question

A bowl contains 4 yellow marbles and 3 red marbles. Eric randomly draws 3 marbles from the bowl. He replaces each marble after it is drawn. What is the probability that he draws 1 yellow marble and 2 red marbles

Answer 1

First draw p yellow = 4/7
2nd draw p red = 3/7
3rd draw p red = 3/7

To find the probability of this event (1yellow 2 red - with replacement) we multiply the probabilities.

4/7 x 3/7 x3/7  = 36/343 which cannot be reduced further

Answer 2

There are 7 marbles in the bowl all together.

-- Probability of a yellow marble on any draw  =  4/7
-- Probability of a red marble on any draw       =  3/7

-- Probability of one yellow and two red in 3 draws = (4/7) (3/7) (3/7) = 36/343

                                                                                     =    10.5%  (rounded)