Florida Pick 3 In the Florida Pick 3 lottery, you can place a ...

Question

Florida Pick 3 In the Florida Pick 3 lottery, you can place a “straight” bet of $1 by selecting the exact order of three digits between 0 and 9 inclusive (with repetition allowed), so the probability of winning is 1/1000. If the same three numbers are drawn in the same order, you collect $500, so your net profit is $499.

a. Find the actual odds against winning.

a. Find the actual odds against winning.

Accepted Answer

Below 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. In a password challenge, a user must correctly guess a 4 digit passcode randomly selected from 0 to 9 digits may repeat. The chances of success is 1 out of 10,000. If the user guesses the exact code, they win a special reward. Find the actual odds against winning. Awesome. So it appears for this particular problem, we're asked to find the actual odds against winning. So, based on all the information that's provided to us by the problem itself, we're trying to determine the actual odds that this user can correctly guess this code. During this password challenge. So with that said, let's read off our multiple choice answers to see what our final answer might be. A is 12 10,000. B is 12 9,999, C is 10,000 to 1, and D is 9,999 to 1. Awesome. So first off, in order to solve this particular problem, we need to understand what the probability of winning will be. So as we should recall a note, the chance of guessing the correct code, the equation can be written as the probability P of winning. So P of win is going to be equal to 1 divided by 10,000 means there's 10,000. Chance, so we're told by the problem itself that there's a chance of success is 1 out of 10,000, so that would be 1 divided by 10,000. Our second step is we need to find the probability of not winning. So as we should recall, the equation to help us solve for the probability of not winning, we could call this P of not win. So P of not winning, so the probability of not winning is equal to 1 minus P of win. Which will mean that this is equal to when we plug in our known variables, 1 minus 1 divided by 10,000, which is going to be equal to 9,999 divided by 10,000. Fantastic. So now our third step is we need to calculate the odds against winning. So as we should recall a note, the odds against winning are expressed as, and we'll denote this as odds against winning, I'll call it OAW, so odds against winning is going to be equal to P of not win. Divided by P of win, which is gonna be equal to 9,999 divided by 1. So that will mean, without a doubt, the actual odds against winning will be 9,999 to 1. And that's it. That is our final answer. Hooray, we did it. So this corresponds to multiple choice answer letter D, which once again is 9,999 to 1. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

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Key Concepts

Probability

Odds

Net Profit

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