Question

There are four red, three green, and five blue discs. Find the probability that the two discs of same color are drawn out

Answer 1

$$4+3+5=12$$

$$P(R,R)=\dfrac{4}{12}\cdot\dfrac{3}{11}=\dfrac{1}{11}$$

$$P(G,G)=\dfrac{3}{12}\cdot\dfrac{2}{11}=\dfrac{1}{22}$$

$$P(B,B)=\dfrac{5}{12}\cdot\dfrac{4}{11}=\dfrac{5}{33}$$

$$P(2\ same)=P(R,R)+P(G,G)+P(B, B)$$

$$=\dfrac{1}{11}+\dfrac{1}{22}+\dfrac{5}{33}=\dfrac{19}{66}$$