In a straight 3 lottery you choose a 3 digit number. A 3 digit number is chosen at random, If your number mataches you win $250.

1. How many diifrent three digit numbers are there? I thought you would do 3^3 but that only equaled 27 so i assumed im wrong

2. what is the proabiliy that your number is the winner

3. There are two outcomes in the sample space {$250,$0} using these write down a probaility model for the straight pick 3 lottery

Please help me im very confused!! Thank you

000 to 999

0 through 9 0 through 9 0 through 9
10^3 = 1000

so
1/1000

I do not know what #3 means either

1. To find the number of different three-digit numbers, you need to consider all possible combinations of digits from 0 to 9 for each position (hundreds, tens, and units place). For the hundreds place, you have 10 choices (0-9), for the tens place, you also have 10 choices, and for the units place, you have 10 choices. To determine the total number of three-digit numbers, you multiply the number of choices for each position together: 10 x 10 x 10 = 1000. So, there are 1000 different three-digit numbers.

2. To calculate the probability of winning, you need to compare the favorable outcomes (winning number matches your chosen number) to the total possible outcomes. Since there is only one winning number, the favorable outcome is 1. From the previous question, we know that the total number of three-digit numbers is 1000. So, the probability of winning is 1/1000.

3. A probability model is a way of showing the likelihood of different outcomes in a random process. In this case, the two outcomes in the sample space are winning $250 and winning $0. To create a probability model, you assign probabilities to each outcome. Let's say the probability of winning $250 is p and the probability of winning $0 is q. Since these two outcomes encompass all possibilities, p + q must equal 1.
Based on the given information, you know that the only winning outcome is $250. Therefore, the probability of winning $250 is p = 1. As a result, the probability of winning $0 is q = 1 - p = 1 - 1 = 0.
The probability model for the straight pick 3 lottery would be:

Outcome: $250 $0
Probability: 1 0