Three red balls from an urn

Text

An urn contains $6$ red balls and $4$ green balls. Three balls are drawn without replacement. What is the probability that they are all red?

Solution

Since the order of drawing does not matter, we use combinations.

• Possible cases: choosing $3$ balls out of $10$: $\binom{10}{3} = 120$.
• Favorable cases: choosing $3$ balls out of the $6$ red ones: $\binom{6}{3} = 20$.

Hence $P = \frac{\binom{6}{3}}{\binom{10}{3}} = \frac{20}{120} = \frac{1}{6} \approx \boxed{0.167}.$