Question

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

Answer 1

So,

The probability of drawing a yellow marble is
`(3)/(7)`.
Since he replaces the marble after it is drawn out, the probability of drawing another yellow is the same:
`(3)/(7)`.

The probability of drawing a red marble is
`(4)/(7)`.

In order to get the probability of drawing 2 yellow marbles and 1 red marble, given that each marble is replaced after it is drawn out, we must multiply the fractions together.


`( (3)/(7) )( (3)/(7) )( (4)/(7) ) = (36)/(343)`

Because the order of the marbles doesn't matter, we will multiply the probability by 3.

`3( (36)/(343) ) = (108)/(343)`