 Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question says two dice are thrown. The events A, B and C are as follows. A is getting an even number on the first die. Event B is getting an odd number on the first die. And even C is getting the sum of the numbers on the die less than equal to 5. Describe the event A dash that is complement of A. So let us start with the solution to this question. We see that when two dice are thrown, the outcome that we have can be 1, 1, 1, 2, 1, 3 that is 1 on the first die and 1 on the second die, 1 on the first die, 2 on the second die, 1 on the first die, 3 on the second die. Similarly, 1, 4, 1, 5, 1, 6 or 2, 1, 2, 2 till 2, 6 that is 2 on the first die, 1 on the second die and so on till 2 on the first die and 6 on the second die and so on. We can have 4, 1, 4, 2 till 4, 6 and so on we have till 6, 6. Now we see that this becomes the sample space for the event when two dice are thrown and these are the respective sample points for this sample space. Now event A was getting an even number on the first die. So we will see that sample space for event A will be all those sample points where the first one is an even number because we are getting an even number on the first die. So the sample space for event A is 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6. Now here we see that we should have an even number on the first die no matter what is the number on the second die and we will have 6, 1, 6, 2, 6, 3, 6, 4, 6, 5 and 6, 6. So these are the sample points and this is the sample space for event A. Now for event A dash the sample points will be all those points which we get by subtracting event A from the sample space. So the points are 1, 1, 1, 2, 1, 3, 1, 4, till 1, 6, 3, 1, 3, 2, till 3, 6 and 5, 1, 5, 2, till 5, 6. So this is the sample space for event A dash and we see that this will be equal to event B that is getting an odd number on the first die in all these sample points. We see that on the first die we are getting an odd number. So this is same as the event B. So this is our answer to the question. I hope that you understood the question and enjoyed the session. Have a good day.