A bag contains certain number of green and pink balls. The ratio of the number of green and pink balls in the bag is 7 : 5 respectively. Two balls are randomly drawn from the bag and the probability that both the balls are pink is \(\frac{1}{6}\). Find the total number of balls in the bag.
Answer & explanation
Correct answer: option 3
Let the number of green and pink balls in the bag are 7R and 5R respectively
The probability that both the balls are pink = \(\frac{^{5} \mathrm{ C }_2}{^{12} \mathrm{C}_2}\) = \(\frac{1}{6}\)
⇒ \(\frac{5R × (5R - 1)}{12R (12R - 1)}\) =\(\frac{1}{6}\)
⇒ R = 3
⇒ So, the total number of balls in the bag = 12× 3 = 36
Hence, option C is correct.