 Hello and welcome to the session. My name is Mansi and I am going to help you with the following question. The question says an experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events. A. The sum is greater than 8. B. Two occurs on either die. C. The sum is at least 7 and a multiple of 3. Which pairs of these events are mutually exclusive. So let us see the solution to this question. First of all let us find out the sample space for the event A, B and C. But first of all we see that if a die is thrown it can turn of 1, 2, 3, 4, 5, 6. Here a pair of dice is rolled. So sample space for the event when a pair of dice is rolled will be 1, 1 that is getting 1 on the first die, 1 on the second die. Similarly 1, 2 getting 1 on the first die and 2 on the second die. Similarly till 1, 6 that is getting 1 on first die and 6 on the second die. Similarly getting 2 on first die and 1 on the second die. And so on we will have till 6, 6. So this is the sample space of the event when a pair of dice is rolled. Now we write down the sample space for the event A. Event A is the sum is greater than 8 so we will consider all the sample points from this sample space where the sum of these two are greater than 8. So the sample points for the sample space of event A will be 3, 6, 4, 5, 4, 6, 5, 4, 5, 5, 6, 6, 3, 6, 4, 6, 5 and 6, 6. So we see that in all these sample points sum of these two is greater than 8. Now we write down the sample space for event B. We see that event B is 2 occurs on either die so the sample space for event B will be 1, 2, 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 3, 2, 4, 2, 5, 2 and 6, 2. Now we write down the sample space for event C. Now even C given to us is the sum is at least 7 and a multiple of 3. So from this sample space this we see that such points are such sample points are 3, 6, 4, 5, 5 is at least 7 that is the sum is 7 or more than 7 and all of them they are multiple of 3. Now we have to tell which pairs of these events are mutually exclusive first of all we consider A intersection B. We see that A intersection B is equal to 5 because no sample points are common to these two sample spaces so the intersection is 5. Now we consider B intersection C again this will be equal to 5 and if we consider A intersection C we see that this is common in both of them 4, 5 is common, 5, 4 is common, 6, 3 is common and this section C is not equal this question is A and B truly exclusive. So this is our answer to the question I hope that you understood the question and enjoyed the session have a good day.