Question

a) Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. The sum is 7, given that the green one is either 6 or 2.

b) Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. The red one is 3, given that the sum is 5.

Answer 1

Two fair dice, one red and one green are rolled.

So, as each dice can have 6 outcomes each, so the number of all possible cases is 6*6, ie. 36.

Question a

The sum is 7, given the green die is either 6 or 2.

Now, if the green die is 6, then the red die is 1.

If the green die is 2, the red die is 5.

So, there are only two favourable cases, for sum 7 and the green die being 6 or 2.

Now, the green die can be 6 or 2, in 2 ways.

So, the required probability is

Question 2

The red one is 3, given the sum is 5.

Now, if sum is 5 and red is 3, green die must be 2.

So, there are 1 favourable cases.

Now, the sum can be 5 if the outcomes are (1,4), (2,3), (3,2), (4,1).

So, there are 4 outcomes.

So, the required probability is