 Hello and welcome to the session. Let's discuss the following question. It says a die is shown. Find the probability of the following events. First one is a prime number will appear. Second is a number greater than or equal to 3 will appear. Third one is number less than or equal to 1 will appear. Fourth one is number more than 6 will appear. And the fifth one is number less than 6 will appear. Before moving on to the solution, let us understand the formula for the probability of any event E, which is the subset of the sample space S. If S is the sample space is any event, then the probability of E is given by the number of outcomes favourable to E upon total number of outcomes. This knowledge will work as key idea. Let us now move on to the solution to find the probabilities of these events. We first need to write the sample space of the experiment of tossing a die. Now we know that whenever we toss a die, there are 6 possibilities and these are possibility of getting 1, 2, 3, 4, 5 and 6. So the total number of outcomes is equal to 6. And in the first case, we have to find the probability of getting a prime number. So here event E is event of getting prime number. Let us now see in the sample space which are the prime numbers. There are 3 prime numbers, 2, 3 and 5. So the number of outcomes favourable to E, favourable are 3. This is 1, 2 and 5. So the probability of getting prime number is equal to the probability of getting prime number is 3 by 6. That is the number of outcomes favourable to upon the total number of outcomes. And in the second case, we have to find the probability of getting a number greater than or equal to 3. So from the sample space, we see that which numbers are greater than or equal to 3. These are 3, 4, 5 and 6. The numbers greater than or equal to 3, E, 4, 5 and 6. So the number of outcomes favourable to E are 4. And we know that the total number of outcomes are 6. So the probability of getting a number greater than or equal to 3 is equal to the number of outcomes favourable to E. That is 4 upon the total number of outcomes that is 6. And in the third part, we have to find the probability of getting a number less than or equal to 1. So here E is the event of getting a number less than or equal to 1. Now we see that which are the outcomes favourable to E and there is only one favourable outcome that is 1. Because on a die, we can get 1. But we cannot get any number less than 1. So the only possible outcome which is favourable to E that is a number less than or equal to 1 is 1. That is we get 1 on a die. So the number of outcomes favourable to E is 1. So the probability of getting a number less than or equal to 1 is equal to the number of outcomes favourable to E that is 1 upon the total number of outcomes which are 6. So the probability is 1 by 6. Now in the fourth part, we have to find the probability of getting a number more than 6. Now from the sample space, we see that there is no possibility of getting a 6 on a die. As we know that whenever we toss a die, we cannot get a number more than 6. So the probability of getting a 6 is more than 6 is 0. So here E is the event of getting a number more than 6 and here the number of outcomes favourable to E is 0 because we cannot get any number more than 6 on a die. So the probability of getting a number more than equal to the number of outcomes favourable to E that is 0 upon the total number of outcomes that is 6. So the probability of getting a number more than 6 is 0. Now in the last part, we have to find the probability of getting a number less than 6. So here we see that there are 5 possibilities of getting a number less than 6 that is 1, 2, 3, 4 and 5. All these numbers are less than 6. So here E is the event of getting a number less than 6 and the outcomes favourable to E are 1, 2, 3, 4 and 5. So the number of outcomes favourable to E is equal to 5 is 1, 2, 3, 4 and 5. So the probability of getting a number less than 6 is equal to the number of outcomes favourable to E which are 5 and upon the total number of outcomes that is 6. So the probability is 5 by 6. So the probability of getting a prime number is 3 by 6 which is equal to 1 by 2 and the probability of getting a number greater than or equal to 3 is 4 by 6 which is same as 2 by 3 and the probability of getting a number less than or equal to 1 is 1 by 6 and the probability of getting a number more than 6 is 0 and probability of getting a number less than 6 is 5 by 6. So the answer to the first part of the question is 1 by 2. To the second part of the question answer is 2 by 3 and to the third part answer is 1 by 6. To the fourth part answer is 0 and to the fifth part answer is 5 by 6. This completes the question and the session. Bye for now. Take care. Have a good day.