Two balls are drawn, from a bag containing 3 red, 4 white and 5 black identical balls. Find the probability that they are all of the same colour.
A. \(\frac{5}{33}\)
B. \(\frac{13}{66}\)
C. \(\frac{8}{53}\)
D. \(\frac{19}{66}\)
Correct Answer: D
Explanation
\(P(\text{two same color balls}) = P(\text{2 red}) + P(\text{2 white}) + P(\text{2 black})\)
\(P(\text{2 red}) = \frac{3}{12} \times \frac{2}{11} = \frac{1}{22}\)
\(P(\text{2 white}) = \frac{4}{12} \times \frac{3}{11} = \frac{1}{11}\)
\(P(\text{2 black}) = \frac{5}{12} \times \frac{4}{11} = \frac{5}{33}\)
\(P(\text{2 same color balls}) = \frac{1}{22} + \frac{1}{11} + \frac{5}{33} = \frac{19}{66}\)
