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: Option 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})