Question

6) An urn contains eight green balls and nine white balls. A sample of four balls is selected at random from the urn.

Answer 1

There is a total of 17 balls in the urn, and there are $\dbinom{17}4=\dfrac{17!}{4!(17-4)!}=2380$ ways of selecting 4 balls from it.

a.

$P(\text{all green OR all white})=P(\text{all green})+P(\text{all white})=\dfrac{\binom84+\binom94}{\binom{17}4}=\boxed{\dfrac7{85}}$

b.

$P(\text{3 green, 1 white OR all green})=P(\text{3 green, 1 white})+P(\text{all green})=\dfrac{\binom83\binom91+\binom84}{\binom{17}4}=\boxed{\dfrac{41}{170}}$