Question

A bag contains 5 red balls and 6 white balls. If we draw 4 balls, find the probability that at least 3 balls are white.

Answer 1

1)

$$P(W=4)=\frac{\binom{6}{4}}{\binom{11}{4}}$$

$$\binom{6}{4}=\frac{6!}{4!2!}=15$$

$$\binom{11}{4}=\frac{11!}{4!7!}=330$$

2)

$$P(W=3)=\frac{\binom{6}{3}}{\binom{11}{4}}$$

$$\binom{6}{3}=\frac{6!}{3!3!}=20$$

3)

$$P(W\ge3)=\frac{15+20}{330}=\frac{7}{66}\approx 0.106$$