In a group of eight students three are female and five are...

In a group of eight students three are female and five are male. If a committee of two is to be selected at random, what is the probability that a. Both members are female?
b. Both members are male?

Key Concepts

Probability

Probability is a field in mathematics that measures how likely an event is to occur. It is generally calculated by dividing the number of favorable outcomes by the total number of possible outcomes in a sample space.

Combination

A combination is a way of selecting items from a larger set where the order in which the items are selected does not matter. Combinations are typically used when the task is to choose groups from a set without considering the arrangement.

Binomial Coefficient

The binomial coefficient is a mathematical formula used to determine the number of ways to select a subset of items from a larger set when the order of selection is irrelevant. It is often denoted as 'n choose k' and is essential for counting the possible outcomes in combination problems.

Sample Space

The sample space is the complete set of all possible outcomes of an experiment or selection process. Accurately identifying the sample space is crucial in probability because it defines the denominator when calculating the probability of an event.

Favorable Outcomes

Favorable outcomes refer to the specific outcomes within the sample space that fulfill the conditions of the event being considered. In probability calculations, the number of favorable outcomes is used to determine the likelihood of that event.

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