 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that Samantha has 20 marbles in a bag and these are 10 red, 4 blue, 3 yellow and 3 green. She randomly selects one marble from the bag. She wins money which is described in the form of given table. What is the expected value of her winning? Here in this table we have two columns, one for marble's color and the second for the amount 1. And if she selects a red marble then she gets $2. For a blue marble she gets $1. For a yellow marble she gets $3. And for a green marble she gets $4. Now let us start with the solution of the given question. We are given that there are 20 marbles in a bag and one marble is drawn at random. And out of the given 20 marbles 10 are red in color, 4 are blue in color, 3 are yellow and 3 are green. Now probability of drawing a red marble will be given by number of outcomes favorable to the event upon total number of outcomes. And here number of outcomes favorable to this event are 10 and total number of outcomes are 20. So we get this probability as 1 by 2. Similarly probability of drawing a blue marble will be equal to 4 upon 20 that is equal to 1 by 5. Probability of drawing a yellow marble will be equal to 3 by 20 and probability of drawing a green marble will be equal to 3 by 20. And in the table we are given the amount 1 when each of the given marble is drawn. Let us denote this amount value by small x. Now we draw a table for the values of small x probability of small x small x into probability of small x. Here the small x values given to us are 2 dollars, 1 dollar, 3 dollars and 4 dollars. And we know that for red marble the amount 1 is 2 dollars. For blue marble the amount is 1 dollar. For yellow marble the amount is 3 dollars. And for green marble the amount is 4 dollars. And probability of drawing a red marble is 1 by 2. Probability of drawing a blue marble is 1 by 5. Probability of drawing a yellow marble is 3 by 20 and probability of drawing a green marble is again 3 by 20. Now we shall calculate small x into probability of small x values. And here we get 2 into 1 by 2 which is equal to 1. 1 into 1 by 5 that is equal to 1 by 5 which is equal to 0.2. 3 into 3 by 20 is 9 by 20 which is equal to 0.45. And 4 into 3 by 20 is 12 by 20 which is equal to 0.6. And we know that expected value of random variable capital X is given by E of capital X is equal to summation of small xi into probability of small xi where i varies from 1 to n so here expected value is equal to summation of small xi into probability of small xi where i varies from 1 to 4. Since the number of observations here are 4 so i varies from 1 to 4. And it can also be written as summation of small x into probability of small x and this is equal to 1 plus 0.2 plus 0.45 plus 0.6 and this is equal to 2.25. Thus we say that expected value of her winning is 2.25 dollars which is a required answer. This completes our session. Hope you enjoyed this session.