Question

Consider a collection of envelopes consisting of 3 red envelopes​, 1 blue envelope​, 2 green envelopes​, and 3 yellow envelopes. If two envelopes are selected at​ random, with​ replacement, determine the probability that at least one envelope is a red envelope.

Answer 1

Answer: The probability that at least one of the envelopes is red is 1/9 (simplified) or 9/81.

Explanation:

There are a total of 9 envelopes. If two are selected at random with replacement the probability for both envelopes is 3 / 9 or 1/3. Since there are two you would do 1/3 * 1/3 to get 1/9 or 3/9 * 3/9 to get 9/81.