Question

If three employees were randomly selected, what is the probability that all three are male?

Answer 1

How can you determine the probability if you don't know how many males and females are in the population from which you are taking the sample of three males? For example, if the population is all male, the probability will always be 100%.

Answer 2

We can find the probability that no women are selected and subtract it from 1 to find the probability that at least one woman is selected. To find the probability that only men are selected, we consider that the chance that the first person selected is male is $\frac{7}{10}$. Then the probability that the second person selected is male is reduced to $\frac{6}{9}=\frac{2}{3}$. For the third person, the probability is $\frac{5}{8}$. So the probability that only men are selected is $$\frac{7}{10}\cdot\frac{2}{3}\cdot\frac{5}{8}=\frac{7}{24}.$$ Notice that the 2 and 5 in the numerator cancel with the 10 in the denominator to leave $\frac{7}{24}$. Now we subtract from 1 to find the probability that at least one woman is selected. The probability is $1-\frac{7}{24}=\boxed{\frac{17}{24}}$.