A roulette wheel has 38 slots and a ball that rolls until it falls into one of the slots, all of which are equally likely. Eighteen slots are black numbers, eighteen are red numbers, and two are green zeros. If you bet on “red,” and the ball lands in a red slot, the casino pays you your bet (i.e. you get your twice your money back); otherwise, the casino wins your bet. (a) What is the expected value of a $1 bet on red? (b) Suppose you bet $1 on red, and if you win you "let it ride" and bet $2 on red. What is the expected value of this plan? (c) Suppose you bet $1 on red, and if you win you "bet your winnings" and again bet $1 on red. What is the expected value of this plan?

A roulette wheel has 38 slots and a ball that rolls until it falls into one of the slots, all of which are equally likely. Eighteen slots are black numbers, eighteen are red numbers, and two are green zeros. If you bet on “red,” and the ball lands in a red slot, the casino pays you your bet (i.e. you get your twice your money back); otherwise, the casino wins your bet. (a) What is the expected value of a $1 bet on red? (b) Suppose you bet $1 on red, and if you win you "let it ride" and bet $2 on red. What is the expected value of this plan? (c) Suppose you bet $1 on red, and if you win you "bet your winnings" and again bet $1 on red. What is the expected value of this plan?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.3: Conditional Probability; Independent Events; Bayes' Theorem

Problem 39E: The following problem submitted by Daniel Hahn of Blairstown, Iowa, appeared in the Ask Marilyn...

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