Question

Two standard six-sided dices are rolled. Find the probability that the numbers are 2 and 4 under the condition that the sum of the numbers is 6.

Answer 1

Let (x1, x2) denote the event that 1st die rolled x1 and second die rolled x2.

Now, we need to find the following probability:

Now, we observe that:

P(die rolled 2 and 4) = P((2,4)) + P((4,2))

= 1/36 + 1/36 (Since each possible combination of numbers is equally likely and there are total 6*6 = 36 possibilities)

= 2/36

P(Sum of the numbers is 6) = P((1,5)) + P((2,4)) + P((3,3)) + P((4,2)) + P((5,1))

= 1/36 + 1/36 + 1/36 + 1/36 + 1/36

= 5/36

Thus,

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