Odds The chances of winning are often written in terms of odds...

Question

Odds The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read "2 to 3"). In Exercises 91-96, use this information about odds.
92. The probability of winning an instant prize game is 1/10. The odds of winning a different instant prize game are 1 : 10. You want the best chance of winning. Which game should you play? Explain your reasoning.

92. The probability of winning an instant prize game is 1/10. The odds of winning a different instant prize game are 1 : 10. You want the best chance of winning. Which game should you play? Explain your reasoning.

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. The probability of a vending machine dispensing a bonus snack is 1/12. The odds of receiving a bonus snack from a different vending machine are 1 to 8. You want to choose the machine with the better chance. Which machine should you pick justify your choice? Awesome. So it appears for this particular problem we're asked to investigate our two different vending machines, and we're asked to choose which machine has a better chance of dispensing a bonus snack, and we're asked to see which one of these machines will be picked that has a better chance of dispensing a bonus snack, and then we're asked to justify our choice, and those are our final pair of answers that we're trying to ultimately solve for. So our first answers are trying to determine which machine are we trying to pick, and then we're asked our second answers we're asked to justify why we made our decision or made our choice. So with that said, let's read off our multiple choice answers to see what our final answer might be. So A is choose the first machine because its probability is higher. B is both machines offer equal chances of success. C is choose the second machine because its odds provide a higher probability, and D is choose the first machine because the odds are better. Awesome. So our first step to solve this particular problem is we need to recall and understand the relationship between odds and probability. If the odds are given as A to B, Then that means the probability of success, which we'll call S for short, so the probability of success is equal to a divided by A plus B. Our second step. we need to evaluate the first machine. So as we should recall, this machine has a probability of a bonus snack when P subscript 1 is equal to 1/12, which is approximately equal to 0.0. 83. Awesome. So now, Our 3rd step. we need to evaluate the second machine based on odds, so we're giving the odds 1. 28, and with our odds 1 to 8, we will have a probability P2, P subscript 2 is equal to 1 divided by 1 + 8, which is equal to 19th, which is approximately equal to 0.111. So now, Our fourth step is we need to compare the two machines, and we will find that 0.111 is greater than 0.083, and once again we rounded both of our probabilities for the 1st and 2nd machine to three decimal places. So we will find therefore, that the second machine offers a better chance of receiving a bonus snack. So that will mean that our final answer without a doubt will have to be multiple choice answer letter C, which states that choose the second machine because its odds provide a higher probability, and that's it. We've officially solved for this problem. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Odds vs. Probability

Calculating Odds

Comparing Odds

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