(b) A Roulette table has numbers from 0 to 36 to place bets on. 18 of them red, 18 of them are black, and one of them is green. In every round, one of the numbers between 0 and 36 is randomly chosen to win. You can place a bet on a single number, or you can place a bet on all red numbers simultaneously. If you place $1 on red and a red number is chosen, you double your money, otherwise you lose your money. If you place $1 on a single number and this number is chosen, you get back $36 (including the $1 you placed), otherwise you lose your money. (i) Calculate the expected value for the money you win if you place $1 on red. What is the expected value for the money you win if you place $1 on a single number? Show all your working. (ii) How much money can you expect to end up with, if you start out with $37 and you place $1 on red 37 times in a row? Justify your answer. (iii) Assume you start with $10 and you place $1 on a single number 10 times in a row. Calculate the probability that you lose all of your money. What is the probability that you win exactly once? Show all your working and justify your answers.

(b) A Roulette table has numbers from 0 to 36 to place bets on. 18 of them red, 18 of them are black, and one of them is green. In every round, one of the numbers between 0 and 36 is randomly chosen to win. You can place a bet on a single number, or you can place a bet on all red numbers simultaneously. If you place $1 on red and a red number is chosen, you double your money, otherwise you lose your money. If you place $1 on a single number and this number is chosen, you get back $36 (including the $1 you placed), otherwise you lose your money. (i) Calculate the expected value for the money you win if you place $1 on red. What is the expected value for the money you win if you place $1 on a single number? Show all your working. (ii) How much money can you expect to end up with, if you start out with $37 and you place $1 on red 37 times in a row? Justify your answer. (iii) Assume you start with $10 and you place $1 on a single number 10 times in a row. Calculate the probability that you lose all of your money. What is the probability that you win exactly once? Show all your working and justify your answers.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

Problem 6ECP: In Pennsylvania’s Cash 5 game, a player chooses five different numbers from 1 to 43. If these five...

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