Indian Institute of Foreign Trade 2008 Solved Paper

There are 3 ways to win money in the game. The number you picked can come up in one dice, 2 dice or 3 dice. The probability of the number you picked coming in all three dice =$\left(\frac{1}{6}\right)\cdot\left(\frac{1}{6}\right)\cdot\left(\frac{1}{6}\right)=\frac{1}{216}$ The probability of the number picked coming on 2 dice = 3C2*$\left(\frac{5}{6}\right)\cdot\left(\frac{1}{6}\right)\cdot\left(\frac{1}{6}\right)=\frac{15}{216}$ The probability of the number picked coming on 1 dice = 3C1*$\left(\frac{5}{6}\right)\cdot\left(\frac{5}{6}\right)\cdot\left(\frac{1}{6}\right)=\frac{75}{216}$Probability of winning = $\left(\frac{1}{216}\right)+\left(\frac{15}{214}\right)+\left(\frac{75}{216}\right)=\left(\frac{91}{216}\right)$ =0.421Therefore, option C is the right answer.