 Hello and welcome to the session. Let us discuss the following question. It says a box contains 20 balls wearing numbers 1, 2, 3 up to 20. A ball is drawn at random from the box. What is the probability that the number on the ball is an odd number divisible by 2 or 3, prime number not divisible by 10. So let's now move on to the solution and we are given that the total number of balls are given to be 20. We have to find the probability that the ball drawn wears an odd number in the first case. Let E be the event of getting a ball wearing an odd number. Now we see that how many odd numbers are there between 1 to 20. That is N E, 1, 3, 5, 7, 9, 11, 13, 15, 17 and these are 1, 2, 3, 4, 5, 6, 7, 8, 9 and also 19. This is also an odd number. So N E is 10. So the probability of getting an odd number is given by the number of outcomes favourable to E. That is N E upon the total number of outcomes. So this is equal to 1 by 2. Now in the second case, let E be the event of getting number divisible by 2 or 3. We see the numbers which are divisible by 2 or 3 and these are 2, 3, 4, 6, 20 and we also have 8 because 8 is divisible by 2 and N E is, that is the number of outcomes favourable to E are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and also 15 is divisible by 3. So it becomes 13. So the probability of getting a number divisible by 2 or 3 is given by number of outcomes favourable to E. That is N E upon the total number of outcomes and there are total number of balls are given to be 20. Now in the third part, we have to find the probability that ball drawn bears a prime number. So let E be the event of getting a ball bearing prime number. Let us see how many numbers are there which are prime between 1 to 20. These are 2, 3, 5, 7, 11, 13 and 17. So the probability of getting a ball bearing prime number is given by the number of outcomes favourable to E. That is N E which is 1, 2, 3, 4, 5, 6, 7 upon the total number of outcomes. Now in the fourth part we have to find the probability of getting a number which bears a number, sorry we have to find the probability of getting a ball which bears a number which is not divisible by 10. So the event of getting a ball bearing a number not divisible by 10. We know that the numbers 1 to 20, 1 to 19 and also 10 is divisible by 10. So 1 to 19 except 10 are the numbers which are not divisible by 10. So there are 18 numbers in all. So the probability that not divisible by 10 equal to the number of outcomes favourable to E that is 18 upon the total number of outcomes that is 20 and this is equal to 9 by 10. So the answer to the first part of the question is 1 by 2, answer to the second part of the question is 13 by 20, answer to the third part of the question is 7 by 20 and answer to the fourth part of the question is 9 by 10, 9 by 10. So this completes the question and the session. Bye for now. Take care. Have a good day.