Question

The Nero Place casino has a new, exciting gambling machine: the multiplying bandit. How does it work? The bandit has a lever or “arm” that the player may depress up to 10 times. After each pull, a H (heads) or a T (tails) appears, each with probability 1/2 . The game is over when heads appears for the first time, or when the player has pulled the arm 10 times. The player wins 2k dollars if heads appears after k pulls (1 ≤ k ≤ 10), and wins 211 = 2, 048 dollars if, after 10 pulls, heads has not appeared. In order to play the game, the player must pay $15. Assume there are 5, 000 games played each week. Use the CLT to approximate the probability that the casino will lose money in a given week

Answer 1

0 Soluticn Consider a Sinqle qame, toral MOURoon by a layer Jel, 5: J2, 22, 23 24 so there a fited poid by he トet X denote the fondcmXau iade depichna tatamou iCn playahime a player in a ame he pobab each even in cven by Pecond drao) Pail, heads 4 P (No heads) P(x") Λο, we have the pn bability di,tribu on Ottuu amount lay by the Couino ?n α given week (theek aho abnstant. tem of 5ta tha Casino enun ech game fo net pofft the Casino

pected amount Of money latby the Cou,00 21 tl t2 Mean μ 60 te Mean Vatwe of money lost by the atino is neoatho Calculated in t« <imi la, y Pefine random Vaiade y· x-15 lamour, or money lost by tu ain。 Varlan ce :/(2.15+3〉.fr 9ナ(22-5+3). ,l 2/0 42+23

+ 144 12 5. 5998 71-44 Where for im come By CL1T, folloa tandard normal oith mean JU and standard devranor .44 045166983

/136 93件6 .09 .16229 : 0 0. 003