In a group of 10 students at a community college, 6 are...

In a group of 10 students at a community college, 6 are freshmen and 4 are sophomores. If a committee of two is selected at random, what is the probability that
a. Both members are sophomores?
b. Both members are freshmen?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Probability as a Ratio of Outcomes

This concept states that the probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In selection problems, once the total number of ways to choose a group is computed using combinations, the favorable subgroup (for instance, all sophomores or all freshmen) is similarly counted and then divided by the overall total.

Combination Counting

This concept involves using binomial coefficients to count the number of ways to select a subset of items from a larger set when the order of selection does not matter. It is fundamental in problems where one must compute how many different committees or groups can be formed, such as choosing 2 students out of 10.

Sampling Without Replacement

This concept refers to the scenario where items are drawn from a set and are not returned before subsequent draws. It affects the probability calculations because each selection changes the composition of the remaining population, which is essential in situations like forming a committee from a group without replacing any member.

Transcript

Please give Ace some feedback