Question

A bag contains four black and five red balls. If three balls from the bag are chosen at random, what is the chance that they are all black?

• A. $\frac{1}{21}$
• B. $\frac{1}{20}$
• C. $\frac{2}{23}$
• D. $\frac{1}{9}$

Answer 1

The correct option is A $\frac{1}{21}$

4 black and 5 red balls to get all black

$P=\frac{{}^4{C}_3}{{}^9{C}_3}=\frac{4}{84}=\frac{1}{21}$