Solution Found!
answer the given questions that involve odds. Finding Odds
Chapter 4, Problem 44BB(choose chapter or problem)
answer the given questions that involve odds. Finding Odds in Roulette?A roulette wheel has 38 slots. One slot is 0, another is 00, and the others are numbered 1 through 36, respectively. You place a bet that the outcome is an odd number. a.?What is your probability of winning? b.?What are the actual odds against winning? 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 $18 and win? d.?How much profit would you make on the $18 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? (.?Recommendation:?Don’t actually try to convince any casino of this; their sense of humor is remarkably absent when it comes to things of this sort.)
Questions & Answers
QUESTION:
answer the given questions that involve odds. Finding Odds in Roulette?A roulette wheel has 38 slots. One slot is 0, another is 00, and the others are numbered 1 through 36, respectively. You place a bet that the outcome is an odd number. a.?What is your probability of winning? b.?What are the actual odds against winning? 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 $18 and win? d.?How much profit would you make on the $18 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? (.?Recommendation:?Don’t actually try to convince any casino of this; their sense of humor is remarkably absent when it comes to things of this sort.)
ANSWER:Step-by-step Solution Step 1 of 4 (a) When rolling a roulette with 38 slots, there are 38 possible outcome. So, the size of the sample space is 38. One slot is 0, another is 00 and others are numbered 1 through 36 giving us a total of 38 numbers. There are 18 odd numbers. Let A denote the event of having odd number as the outcome in roulette. There are 18 ways that A can occur. Calculating the probability of A: number if ways A occur P(A)= sample space P(A)= 18=9/38 = 0.473 38 Therefore, the probability of winning when placing a bet that the outcome is odd in the roulette is 0.473.