Question: 26 Numeric 5 points In this class we have 21 students, 6 of those are male. If I selected three…

26 Numeric 5 points

In this class we have 21 students, 6 of those are male. If I selected three students from the class at random to perform an experiment, what is the probability that all three students were male?

0.015

27 Numeric 4 points

The average one-way commuting time in Richmond, Virginia is 24.8 minutes with a standard deviation of 4.4 minutes.

Solution

In this problem, we have 21 students, of which 6 are male. We need to find the probability that when selecting three students at random, all three are male. First, calculate the total number of ways to choose 3 students from 21. \[ \binom{21}{3} = \frac{21 \times 20 \times 19}{3 \times 2 \times 1} = 1330 \] Next, calculate the number of ways to choose 3 male students from the 6 males. \[ \binom{6}{3} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20 \] The probability that all three selected students are male is the ratio of the favorable outcomes to the total outcomes. \[ P(\text{all male}) = \frac{\binom{6}{3}}{\binom{21}{3}} = \frac{20}{1330} = \frac{2}{133} \] So, the probability that all three students selected are male is \( \frac{2}{133} \).