 Hi and welcome to the session. Let us discuss the following question. Question says a game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and these are equally likely outcomes. What is the probability that it will point at 8? What is the probability that it will point at an odd number? What is the probability that it will point at a number greater than 2? What is the probability that it will point at a number less than 9? This is the given figure 15.5. First of all, let us understand that probability of occurrence of an event E denoted by Pe is defined as number of outcomes favourable to E upon total number of possible outcomes. This is the key idea to solve the given question. Let us now start with the solution. Now clearly we can see we have 8 numbers and arrow can point any of the number in 8 ways. So total number of possible outcomes is equal to 8. Now in the first part of the given question we have to find the probability that game of chance will point at 8. Clearly we can see that there is only 1 8 on the spinning wheel. So it can be chosen only in one way. So therefore number of outcomes favourable to 8 is equal to 1. From key idea we know probability of an event E is equal to number of outcomes favourable to E upon total number of possible outcomes. So probability of getting 8 is equal to number of outcomes favourable to 8 upon total number of possible outcomes that is 1 upon 8 we know number of outcomes favourable to 8 is equal to 1 and total number of possible outcomes is equal to 8. So probability of getting 8 is equal to 1 upon 8. So required answer for the first part is probability that the game will point at 8 is equal to 1 upon 8. This completes the first part of the given question. Let us now start with the second part. Now we have to find the probability that game will point at an odd number. Clearly we can see we have four odd numbers in the game that is 1, 3, 5 and 7. So we can write there are four odd numbers in the game that is 1, 3, 5 and 7. Now clearly we can see one odd number can be chosen in four ways. So number of outcomes favourable to an odd number is equal to 4. Now let us find out probability of getting an odd number. It is equal to number of outcomes favourable to an odd number that is 4 upon total possible outcomes that is 8. Now we will cancel common factor 4 from numerator and denominator both and we get probability of getting an odd number is equal to 1 upon 2. So required answer for the second part is probability that game will point at an odd number is equal to 1 upon 2. Let us now start with the third part. Now we have to find the probability that game will point at a number greater than 2. Now clearly we can see there are six numbers greater than 2. They are 3, 4, 5, 6, 7, 8. So we can write six numbers greater than 2 are 3, 4, 5, 6, 7 and 8. Out of these six numbers one number can be chosen in six ways. So number of outcomes favourable to an event number is greater than 2 is equal to 6. Now we will find out probability of getting a number greater than 2. It is equal to number of outcomes favourable to an event number is greater than 2 that is 6 upon total number of possible outcomes. Total number of possible outcomes is 8. Now we will cancel common factor 2 from numerator and denominator both and we get probability of getting a number greater than 2 is equal to 3 upon 4. So required answer for the third part is probability that the game will point at a number greater than 2 is equal to 3 upon 4. Let us now start with the fourth part of the given question. Now we have to find the probability that game will point at a number less than 9. Now clearly we can see all these numbers are less than 9. So an event that game will point at a number less than 9 is a sure event. So we can write game will point at a number less than 9 is a sure event and we know probability of a sure event is equal to 1. So probability of getting a number less than 9 is equal to 1. So required answer for the fourth part of the given question is probability that game will point at a number less than 9 is 1. This is our required answer. This completes the session. Hope you understood the solution. Take care and keep smiling.