Consider the random experiment of rolling a pair of fair dic

Consider the random experiment of rolling a pair of fair dice. What is the probability that the sum of the two numbers facing up is equal to 6 given that exactly one of the dice has the number 2 facing up? Round to two Decimals.

Solution

We can get 6 when both the dice have 3, or when either has 4 and the other has 2 or when either has 5 and the other has 1. Also, here we use the property that the probability that two events take place together is the product of their individual probabilities.

Also.it is given that 2nd dice shows 2,so, we can discard when both the dice have 3,or when either has 5 and the other has 1.

We are left with only one case when either has 4 and the other has 2 .

Now the probability of any number when a die is thrown is 1/6. Let