I have two six-sided dice, each with faces numbered from 1 to 6. One of the dice is fair, but the other is not – it will land on numbers 1 to 5 with equal probability, but lands on 6 with a different probability. When I roll the dice the probability that I get a total of 12 is 1/18.
What is the probability that I get a total of 2 when I roll the dice?

Answer:

24) B

Only way to get a total of 12 is to get 6 on both dices.
Since first die is fair, probability of getting a 6 = 1/6

We know probability of getting a total of 12 is 1/18.
We get 1/18 when we multiply probability of 6 on first die with probability of 6 on the second die.
Therefore, probability of getting a 12 on second die = 1/18 ÷ 1/6 = 6/18 = 1/3

Probability of getting other numbers = 1 – 1/3 = 2/3

Only way to get a total of 2 is if we get 1 on first die and 1 on the second die.
Since 1 to 5 have the same probability, probability of getting a 1 on the second die = 2/3 ÷ 5 = 2/15
Probability of getting a 1 on first die = 1/6

Probability of getting a total of 2 = 1/6 x 2/15 = 2/90 = 1/45
Hence, B is the answer.