54.6k views
2 votes
Three marbles are chosen from an urn that contains 6 red, 4 white, and 5 blue marbles. How many samples containing at least 2 blue marbles are possible?

User Dimsuz
by
8.5k points

1 Answer

4 votes

Final answer:

The number of samples containing at least 2 blue marbles is 110.

Step-by-step explanation:

To find the number of samples containing at least 2 blue marbles, we need to consider the different combinations of choosing marbles from the urn. In this case, we can have:

  • 2 blue marbles and 1 marble that is not blue
  • 3 blue marbles

First, let's consider the case of 2 blue marbles and 1 marble that is not blue. We can choose 2 blue marbles from the 5 blue marbles in the urn in C(5, 2) = 10 ways. For the marble that is not blue, we can choose it from the remaining marbles in the urn, which include the 6 red marbles and 4 white marbles. So, we can choose this marble in C(10, 1) = 10 ways. Therefore, the number of samples with 2 blue marbles and 1 marble that is not blue is 10 * 10 = 100.

Now, let's consider the case of 3 blue marbles. We can choose 3 blue marbles from the 5 blue marbles in the urn in C(5, 3) = 10 ways. Therefore, the number of samples with 3 blue marbles is 10.

Adding up the two cases, the total number of samples containing at least 2 blue marbles is 100 + 10 = 110.

User Bill Kary
by
7.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories