If 3 balls are drawn at random from a bag containing 3 red and 4 blue balls, what is the expected number of red balls in the sample?

The expected number of red balls in the sample is 1.2857.

Step-by-step explanation:

The balls are chosen without replacement from the sample, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

The expected value of the hypergeometric distribution is:

3 red balls in the sample:

This means that

3 balls are drawn:

This means that

Total of 3 + 4 = 7 balls:

This means that

What is the expected number of red balls in the sample?

The expected number of red balls in the sample is 1.2857.