 Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question says, a die is rolled, let E be the event, die shows 4 and F be the event, die shows even number. Are E and F mutually exclusive? So let us start with the solution to this question. So now we consider the experiment of rolling a die. The results or outcomes of this experiment are 1, 2, 3, 4, 5 or 6. So the set of outcomes that is this set is called the sample space of the experiment. Any subset E of a sample space S is called an event. So we see that event E is that the die shows 4 so that will be 4. This is an event of getting 4. Also F will be the event when the die shows even number. So F is the event of getting 2, 4 or 6. Now we have to tell that whether E and F are mutually exclusive or not. So we say that E and F are mutually exclusive if E intersection F is equal to 5. Now intersection of 2 sets is set of those elements which are common to both E and F. So we see that elements that are common to E and F are only 4. So it is only 4. So we can say that E intersection F is 4 that is not equal to 5. So E and F are not mutually exclusive. So our answer to this question is no. So I hope that you understood the question and enjoyed the session. Have a good day.