 Hello and welcome to the session. In this session we shall discuss the following question and the question says that a scratch ticket game has the probability distribution that is shown in the given table. In the A part of the question we need to find the expected value for the scratch game and B part of the question says if the player played this game 100 times then what is the expected value. Now let us start with the solution of the given question. In this question probability distribution of a scratch ticket game is given to us where let the price values be small x and corresponding probability be probability of small x that is p of small x. So we draw a table for the values of small x probability of small x and small x into probability of small x and here the small x values that are given to us are 2, 1, 3, 4 and 5 and their corresponding probability values are 2 upon 10, 4 upon 10, 1 upon 10, 2 upon 10 and 1 upon 10. Now we shall find the values for small x into probability of small x and here we get 2 into 2 by 10 which is equal to 4 by 10. Here we have 1 into 4 by 10 that is equal to 4 by 10, 3 into 1 by 10 which is equal to 3 by 10, 4 into 2 by 10 which is equal to 8 by 10 and next we have 5 into 1 by 10 that is equal to 5 by 10. Thus we have got all the values for small x into probability of small x and we need to find the expected value for this scratch game and expected value is given by the formula summation of small x into probability of small x. So here we get 4 by 10 plus 4 by 10 plus 3 by 10 plus 8 by 10 plus 5 by 10 and this is equal to 24 by 10 that is equal to 2.4. Thus expected value for this ticket game is 2.4 dollars. Now the B part of the question says if the player played this game 100 times then what is the expected value? Now if the player played this game 100 times then the expected value will be equal to 2.4 into 100 dollars that is equal to 240 dollars and this averages to 2.4 dollars per game which is the required answer. This completes our session. Hope you enjoyed this session.