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 $\frac{3}{7}$.
Since he replaces the marble after it is drawn out, the probability of drawing another yellow is the same: $\frac{3}{7}$.

The probability of drawing a red marble is $\frac{4}{7}$.

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.

$( \frac{3}{7} )( \frac{3}{7} )( \frac{4}{7} ) = \frac{36}{343}$

Because the order of the marbles doesn't matter, we will multiply the probability by 3.
$3( \frac{36}{343} ) = \frac{108}{343}$