 Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question says three coins are tossed. Describe two events which are not mutually exclusive. Let us start with the solution. First of all we find out the sample space for the event when three coins are tossed. Let H, let H be denoted by H and tails be denoted by T. So the sample space for this event will be H, H, H, H, H, H, H, H, T, H, T, H, H, H, T, H, H, T, H, T, H, and T, T, T. That is getting three heads on three coins. This is getting heads in first two coins and tail in the third and so on. This is getting three tails in three coins. So now we have to tell two events which are not mutually exclusive. So let A be the event of getting at most two tails. That will be the events or that will be the elements where we have 0, 1 or 2, H, H, this is the sample space for the event A that will be H, H, H, H, H, T, H, H, T, H, T, H, T, H, T and T, T, H. We will not consider T, T, T because there are three tails that is more than two. Now let B be the event of getting exactly two tails. So the elements where we have exactly two tails is H, T, T, T, H, T and T, T, H. So the sample space for the event B will be H, T and T, T, H. Now to see whether these two events are mutually exclusive or not, we consider the intersection B. Now A intersection B will be all the elements that are common to both A and B. So the elements common to A and B is here we see we have H, T, T here also we have H, T, T. We have T, H, T here also we have T, H, T and we have T, T, H here also we have T, T, H. So we see that A intersection B is not equal to 5. We have three elements in this also. Therefore intersection B is not equal to 5. So they are not mutually exclusive. So our answer to the question is getting at most two tails, getting exactly two tails. So this is the solution to the question. I hope that you understood the question and enjoyed the session. Have a good day.