(Chapters 5 thru 8 ) This test: 20 point(s) possible For a lottery game, a player must match a sequence of three repeatable numbers, ranging from 0 to 9 , in exact order (for example, 3-7-2). With a single ticket, what is the probability of matching the three winning numbers?

To determine the probability of matching the three winning numbers in a lottery game where each number can range from 0 to 9, we first need to calculate the total number of possible combinations of three numbers. Since each of the three numbers can be any digit from 0 to 9, there are 10 possible choices for each number. Therefore, the total number of combinations for the three numbers is calculated as follows: \[ \text{Total combinations} = 10 \times 10 \times 10 = 10^3 = 1000 \] Now, since there is only one winning combination (the specific sequence of three numbers drawn), the probability of matching the winning numbers with a single ticket is given by the ratio of the number of successful outcomes (1) to the total number of possible outcomes (1000): \[ \text{Probability} = \frac{\text{Number of successful outcomes}}{\text{Total number of outcomes}} = \frac{1}{1000} \] Thus, the probability of matching the three winning numbers with a single ticket is: \[ \frac{1}{1000} \text{ or } 0.001 \]