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.

1 Answer
Lotusbluete
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(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%#

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