An urn contains 5 red marbles, 6 white marbles, and 9 blue marbles marbles. A child randomly selects three (without replacement) from the urn. Round to four decimal places. Find the probability all three marbles are the same color. Find the probability that none of the three marbles are white.

Sure, let's solve these problems step by step.

1. Find the probability all three marbles are the same color.

First, we need to find the total number of marbles in the urn. We have 5 red marbles, 6 white marbles, and 9 blue marbles. So, the total number of marbles is 5 + 6 + 9 = 20.

The probability that all three marbles are the same color can be calculated by adding the probabilities of each color.

• The probability that all three marbles are red is (5/20) * (4/19) * (3/18) = 0.0132.
• The probability that all three marbles are white is (6/20) * (5/19) * (4/18) = 0.0263.
• The probability that all three marbles are blue is (9/20) * (8/19) * (7/18) = 0.1325.

So, the total probability that all three marbles are the same color is 0.0132 + 0.0263 + 0.1325 = 0.1720.

2. Find the probability that none of the three marbles are white.

The probability that none of the three marbles are white can be calculated by subtracting the probability that at least one marble is white from 1.

• The total number of ways to draw three marbles from the urn is 20 choose 3 = 1140.
• The total number of ways to draw three marbles that are not white is 14 choose 3 = 364.

So, the probability that none of the three marbles are white is 364/1140 = 0.3193.

So, the probability all three marbles are the same color is 0.1720 and the probability that none of the three marbles are white is 0.3193.