Question

An urn contains 11 ball: 2 red, 4 blue, 5 green. One ball is removed, with uniform probability. Let R, B, G denote three different events: the ball chosen is red, blue, or green respectively. Find: p(R), p(Bc), p(R ∪ B), p(B ∩ G), p(Rc ∩ Bc), p(Bc ∪ Gc).

Answer 1

$p(R)=\frac{2}{11}$

$p(B^{c})=1-p(B)=1-\frac{4}{11}=\frac{7}{11}$

$p(R\cup B)=p(R)+p(B)=\frac{2+4}{11}=\frac{6}{11}$

$p(B\cap G)=0$

$p(R^{c}\cap B^{c})=p\left ( (R\cup B)^{c} \right )=1-\frac{6}{11}=\frac{5}{11}$

$p(B^{c}\cup G^{c})=p\left ( (B\cap G)^{c} \right )=1-p(B\cap G)=1-0=1$