A modified roulette wheel has
slots. One slot is 0, another is 00, and the others are numbered 1 through
respectively. You are placing a bet that the outcome is an
number. (In roulette, 0 and 00 are neither odd nor even.)
a. What is your probability of winning?
The probability of winning is
(Type an integer or a simplified fraction.)
b. What are the actual odds against winning?
The actual odds against winning are
c. When you bet that the outcome is an
number, the payoff odds are 1:1. How much profit do you make if you bet
and win?If you win, the payoff is
d. How much profit should you make on the
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?
(Round to the nearest cent as needed.)
a) As 0 and 00 are neither odd nor even and the rest 26 slots
have numbers from 1 to 26. Therefore the probability of winning is
computed here as:
= P(Even number)
therefore 13/28 is the required probability here.
b) The actual odds against winning is computed here as:
= Number of outcomes of losing / Number of outcomes of winning
= 15 / 13
therefore 15:13 are the required odds here.
c) Given the payoff odds is 1:1, the profit made when we win is the same as the betting amount computed as $18. Therefore the total payoff here is $18.
d) In case the odds are changed to the actual probability odds, the amount won is computed in that case is:
= Odds of winning * Bet amount
Therefore $20.77 is the profit amount in that case.
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