# A bag contains 3 red, 5 yellow, and 7 purple marbles. What is the probability of drawing a purple marble followed by a red marble?

## The first marble is put back in the bag between draws.

Feb 10, 2016

The probability is about 9.33%.

#### Explanation:

First draw:

You have $15$ marbles in total and $7$ purple ones.
Thus, the probability for the first marble to be purple is

$P \left(1 \text{st marble is purple}\right) = \frac{7}{15}$.

Second draw:

Since you have put the first marble back in the bag, you still have $15$ marbles in total. However, there are only $3$ red ones.
Thus, the probability to draw a red marble is

$P \left(2 \text{nd marble is red}\right) = \frac{3}{15}$

As these two events are independent, you just need to multiply the two probabilities:

$P \left(1 \text{st marble is purple and "2"nd marble is red") = P(1"st marble is purple") * P(2"nd marble is red}\right)$

= 7/15 * 3 / 15 = 7 / 15 * 1 / 5 = 7/75 ~~ 0.0933 ~~ 9.33%