Expected Value for the Florida Pick 3 Lottery In the Florida P...

Question

Expected Value for the Florida Pick 3 Lottery In the Florida Pick 3 lottery, you can bet $1 by selecting three digits, each between 0 and 9 inclusive. If the same three numbers are drawn in the same order, you win and collect $500.

b. What is the probability of winning?

b. What is the probability of winning?

Accepted Answer

Welcome back, everyone. A game show has a digital lock with a 3 digit code. Each digit ranges from 0 to 9. A contestant pays $1 to get the correct code. If the exact sequence is guessed correctly, they win $750. What is the probability of winning? A says 0.100, B 0.010, C 0.001. And the 0.050. We want to calculate the probability of winning, so let's suppose that event A represents winning. The probability of A is simply the ratio between M and M. Where M is the number of favorable outcomes. And N is the total number of outcomes. So now what is um There's only one favorable outcome because there's only one correct 3 digit code, right? And now to identify N or the total number of outcomes, we want to identify the number of ways to form a 3 digit code given elements between 0 and 9 inclusive. So we have a total of 10 elements, right? 9 minus 0 + 1. So now what we're going to do is simply use the multiplication rule. Essentially, since our digits may repeat, then our first digit can be between 0 and 9, which gives us 10 possibilities. The second digit can also be between 0 and 9. This gives us 10 possibilities, and for the third digit, again, we have 10 possibilities. So the multiplication rule says that the total number of ways would be 10, multiplied by 10, multiplied by 10, which is 1000. So we have 1000 possible ways to form a three digit code, meaning the probability of A is the ratio between M and N or 1 and 1000. Which is 0.001, meaning the correct answer corresponds to the answer choice C. Thank you for watching.

��app