Question

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.

Answer 1

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(1"st marble is purple") = 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(2"nd marble is red") = 3/15`

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

`P(1"st marble is purple and "2"nd marble is red") = P(1"st marble is purple") * P(2"nd marble is red")`

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