 Hello and welcome to the session. The question says a die has two faces each with numbers 1, 3 faces each with number 2 and 1 face with number 3. If die is rolled once, determine first probability of the event 2, second probability of 103, third probability of not 3. Let's now start with the solution. Now as we know a die has 6 faces. Well, two faces has number 1 on it, faces has number 2 on it and one face has number 3 on it. Now the die is rolled once, then possible number of total outcomes are 6. Since a die has 6 faces, first let us denote the event E by the face with 2 appears on it. So here the number of favorable outcomes are since 3 faces has number 2 on it. So if a die is rolled once, then the possible number of outcomes are 3. So the probability of event E, that is probability of getting a number 2 when a die is rolled once is the number of favorable outcomes upon the total number of outcomes. Now let us substitute the values. Number of favorable outcomes are 3 and total possible outcomes are 6. So in simplifying we get 1 upon 2. So the answer to the first part is half. Now let us proceed on to the second part where we have to find probability of 1 or 3. Here let us first denote E as the event of face with 1 appears on it and F face with 3 appears on it. So number of favorable outcomes, the event E is equal to 2. Since when a die is rolled, then the possible number of outcomes of getting a 2 is, sorry, getting a 1 is 2. And the number of favorable outcomes of the event E, that is when a die is rolled then the possible number of favorable outcomes for the event F is 1. Since one face has number 3 on it. Therefore probability of E is 2 upon 6, that is number of favorable outcomes upon the total possible number of outcomes and probability of F is 1 upon 6. Now we have to find probability of E or F. So this is equal to probability of E plus probability of F. Since our mutually exclusive events, that is no face on the die has the number 1 and 3 both. So the two events are mutually exclusive, that is if 3 appears then 1 will not appear and if 1 appears then 3 will not appear. Now let us substitute the values of probability of E and probability of F, that is 2 upon 6 plus 1 upon 6 which is equal to 3 upon 6. Now on simplifying we get half. So the answer to the second part, that is probability of 1 or 3 is equal to 1 by 2. So this completes the second part. And now proceeding on to the third part, here we have to find probability of not 3. So first let us denote the event E by the face with 3 appears on it and here the number of favorable outcomes as we have done in the previous part also is equal to 1. The total possible outcomes are 6 since the die has 6 faces. Therefore probability of event E is equal to number of favorable outcomes that is 1 upon the total number of possible outcomes which are 6. So the probability of not 3 we have to find, that is probability of not the event E. And this is equal to 1 minus probability of the event E which is equal to 1 minus 1 upon 6 which is equal to 5 upon 6. Hence the answer to the third part that is probability of not occurring at 3 when a dice is thrown is 5 upon 6. So this is the answer to the last part. Hope you have understood it well. Take care and have a good day.