Question

Two dice are tossed one after the other. What is the conditional probability that the first die is six, given that the sum of the dice is seven?

Answer 1

Given that two dice are tossed one after the other.

We need to find the conditional probability that the first die is six, given that the sum of the dice is seven.

Before we go on to solve the problem let us a bit about conditional probability,

Conditional Probability

For two events A and B the conditional probability of the event A given the event B is given by,

Coming back to our problem

Now the total number of possible outcomes when two dice are tossed=6²=36.

Let us define two events,

Now,

Now only possible outcome of getting the first die as six and the sum of the dice is seven is (6,1).

Now,

Now possible outcomes of getting the sum of the dice as seven is (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) i.e. 6 possible outcomes.

Hence the conditional probability that the first die is six, given that the sum of the dice is seven.

Hence the conditional probability that the first die is six, given that the sum of the dice is seven is 1/6