 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that At a local carnival, there is a spinner with 6 sectors. If the spinner lands on a blue sector, you win $5. If it lands on a yellow sector, you win $3. If it lands on any other sector, you lose $2. Is this game fair? We know that a game in which the expected value for the player is 0, that is, there is no net gain or loss, is a fair game. With this key idea, we shall proceed to the solution. In this question, we are given a spinner with 6 sectors with equally likely possibilities. It means there are 6 equally likely outcomes. Its sample space S is given by the set containing yellow sector, blue sector and 4 other sectors. Now let us draw a probability distribution table for single spin of the spinner and the amount 1. Let small x denotes the amount 1. So here in the probability distribution table, we have taken color in first column, the amount which is given by small x in the second column and the probability values in the third column. Now for yellow color, the probability will be given by 1 upon 6 as there is one sector showing yellow color and there are 6 sectors in all. Similarly, for color blue, the probability will be equal to 1 by 6 as there is one sector showing blue color and for the remaining 4 sectors, the probability will be equal to 4 by 6. Now we shall use formula to calculate the expected value which is given by e of capital X is equal to summation of small x into probability of small x. And here this is equal to 3 into 1 by 6 plus 5 into 1 by 6 plus minus of 2 into 4 by 6 and this is equal to 3 by 6 plus 5 by 6 minus of 8 by 6. And this is equal to 3 plus 5 minus of 8 the whole upon 6 which is equal to 8 minus 8 whole upon 6 that is equal to 0 upon 6 which is equal to 0. So here the expected value is equal to 0. Thus from the key idea we can say that this game is fair which is the required answer. This completes our session. Hope you enjoyed this session.