Question

Sampling students A statistics class with 30 students has 10 males and 20 females. Suppose you choose 3 of the students in the class at random. Find the probability that all three are female.

Short answer

$\text{The required probability is}0.281\text{.}$

Step-by-step solution

Step 1:Given information

Number of males$=10$

Number of females$=20$

Number of students being selected $=3$

Step 2:Calculation

The probability that all three females are selected can be calculated as:

$P($Three females are selected $)=\frac{{}^{20}C_3}{{}^{30}C_3}$

$=\frac{\frac{20!}{(20-3)!\times 3!}}{\frac{30!}{(30-3)!\times 3!}}$

$=\frac{1140}{4060}$

$=0.281$

$\text{The required probability is}0.281\text{.}$