Question

Asked Jul 31, 2019

Two fair dice are rolled at once. Find the conditional probability that the sum is 6, given that the sum is an even number.

Step 1

**Concept of conditional probability:**

For any two events *A *and *B *with *P*(*B*) >0, the formula for conditional probability is given by:

Step 2

**Find the sample space:**

*Sample space:*

The set of all possible outcomes of a probability experiment is called sample space of the experiment.

Here, two fair dice are rolled.

The total number of outcomes in the sample space be *n*(*S*) = 6^{2} = 36. That is, there will be 36 equally likely outcomes.

Outcomes will be occurred in ordered pairs. First number in each ordered pair represents the number on the first die and second number in each ordered pair represents the number on the second die. Each of the two numbers can take values 1 to 6.

The sum of the numbers on the dice will be 2, 3, 4, 5, 6, 7, 8, 9, 10,11 and 12.

The sample space for the experiment is given below:

Step 3

**Find the conditional probability that the sum is 6, given that the sum is an even number:**

There are 5 different ways the sum of the two dice is 6 and 18 different ways the sum of the two dice is an ...

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