In this question for started the first part. They have said that whole game there are 38 tickets. The tickets okay, that are marked plus $2 and, uh, 26 tickets. Meta marked minus $1 in the books. Such chance off drawing plus $2 over Shores has to be 12. Jan's will be 12 out of 38 and we'll hear the Johns. It's going to be 26 out of 28 right now. Some of the numbers in the box We're going to calculate them so we can say this will be equal to 12 in tow. $2. And, uh, plus, we have 26 into minus $1. Right? So this actually gives us the average or the summer's negative toe, also, to find the average off numbers in the box now, so that is going to be minus $2 that were formed upon total, which is 38 so for simplified against it as minus $0.5. Moving further, they have said that the number of roller places 100 so I would write down the number off Roll it please is given as 100 waas, so the expected value for the net gain is a number off draws. Therefore, the expected value for the next game Well here is given by the number off the laws right into the average off the books. So number of draws enormous 100 average of the books if guys late as it is minus $0.5. So it actually comes to be minus $5 or here. So we therefore say that we are expecting a loss off $5 and moving for the and what do now, huh? Talk about the standard division of the books so we can see that the standard deviation off the box when the tickets in the boss show only two different numbers. Big and small. This is going to be equal to the big number, minus D small number. Okay. On. Until we dick squared off, the fraction meant the big number, okay. And into the fraction with this morning number. Right now, the big number we know is $2. Okay. And minus the smaller number we know is $1. It's actually minus $1 and in tow, squared off. We have the faction for the first big numbers 12 by 38 into for the others, 26 by 38. And, uh, so if you simplify, this gives you $3 in tow. This part if you saw, we get 0.47 So approximate value I'm getting here is $1.41. As a standard illusion Nobiz on this, I'm going to find out the standard editor also. So the standard error is given by square root off number of drawers into the standard deviation off the box we just found. Right. So this is square root off. The number of draws is 100 into this is $1.41. So any multiply, we get this approximately as $14. This is an approx value. Okay, Now, therefore, I would like to conclude that in 100 please the gamblers next game, we'll be around minus $5 give our big will be approximately $14. No going on to the next part for the Barbie. We're supposed to now count the number of friends in the game, so I'm going to use a box, uh, like this over here. I'm going it. Someone to have 12 tickets, which will be off one option and 26 tickets, which will be off auction. Zero. All right now, this game is in the average off. The books will be equal to begin to 12 into one, unless we have 26 in true zero on the whole thing, divided by 28. So they sold us their living this value approximately as 0.31 So therefore, expected value for the some off 100 such draws. So there's a vehicle 200 into 0.31 which approximately gives me 31 now for the after. Some careful it the standard division. So the standard deviation the formalize again one minus zero the values on in tow. The factions off the provided He's just well by 38 26 by 28. So this is going to be a zero point for seven. Next time. Finding is the standard editor just squared off. Number off draws into the standard deviation of the box. So this is against squared off 100 Indo 0.47 spaces, approximately five like so well. Therefore say that in 100 please. The gambler should win 21 times, give or take five or so. Right? Okay. Moving on to the last part, which is the part. See off this question. So we see that in single normal play, you can expect Oh knows around, uh, see, $25 in 100 place. Okay, So as a number off place increases to 1000 we say that as the number off plays increases true, 1000. We should expect the laws to be, uh, around $50 like they've been 25 in tow. That 25 4 100 flights so to 54,000 place. And that is more replay. The more we lose. So we conclude that more we play more me to lose here. Okay. So therefore, if you consider the column back, there's much instrument again. So if you consider the column bed, then that is more chance. Go win this game.