A modified roulette wheel has 44 slots. One slot is 0, another is 00, and the others are numbered 1 through 42, respectively. You are placing a bet that the outcome is an odd number. (In roulette, 0 and 00 are neither odd nor even.)
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Part 1
a. What is your probability of winning?
The probability of winning is
. 477.
(Type an integer or a simplified fraction.)
Part 2
b. What are the actual odds against winning?
The actual odds against winning are
23:
21.
Part 3
c. When you bet that the outcome is an odd number, the payoff odds are 1:1. How much profit do you make if you bet $12 and win?
If you win, the payoff is $
enter your response here.
Part 4
d. How much profit should you make on the $12 bet if you could somehow convince the casino to change its payoff odds so that they are the same as the actual odds against winning?
$
enter your response here (Round to the nearest cent as needed.)