Question

A bag contains 3 red, 4 white and 5 blue balls. All balls are different. Two balls are drawn at random. The probability that they are of different colour is

A.  \(\frac{47}{66}\)

B. \(\frac{10}{33}\)  

C. \(\frac{1}{3}\) 

D. 1

Answer 1

As there are 3 +4+5 = 12 balls. 

So, 2 balls out of 12 can be drawn in ¹²C₂ ways = 66 

Let E denote the event that balls drawn are of different colours 

Either the balls will be red-white or white-blue or red-blue.

Hence,

P(E) = 47/66 

As our answer matches only with option (a) 

∴ Option (a) is the only correct choice.