stion 4 of 7 , Step 1 of 1 Isider all four-digit numbers that can be made from the digits \( 0-8 \) (assume that numbers cannot start with 0 ). What is the probability of choosing a randam nu n this group that is greater than 2000 ? Enter a fraction or round your answer to 4 decimal places, if necessary.

To find the probability of choosing a random number from the group of four-digit numbers that can be made from the digits \(0-8\) (excluding numbers that start with 0) and is greater than 2000, we need to first determine the total number of such numbers and then find the number of numbers greater than 2000. Let's start by finding the total number of four-digit numbers that can be made from the digits \(0-8\) excluding numbers that start with 0. The first digit can be any of the digits \(1-8\) (since we exclude 0 as the first digit), and the remaining three digits can be any of the digits \(0-8\). Therefore, the total number of four-digit numbers is \(8 \times 9 \times 9 \times 9 = 5832\). Next, we need to find the number of four-digit numbers greater than 2000. To do this, we can consider the numbers from 2000 to 9999. The first digit can be any of the digits \(2-9\), and the remaining three digits can be any of the digits \(0-8\). Therefore, the number of four-digit numbers greater than 2000 is \(7 \times 9 \times 9 \times 9 = 5103\). Now, we can calculate the probability of choosing a random number from the group that is greater than 2000 by dividing the number of numbers greater than 2000 by the total number of four-digit numbers. \[ \text{Probability} = \frac{5103}{5832} \] Let's calculate this probability. Calculate the value by following steps: - step0: Calculate: \(\frac{5103}{5832}\) - step1: Reduce the fraction: \(\frac{7}{8}\) The probability of choosing a random number from the group of four-digit numbers that can be made from the digits \(0-8\) (excluding numbers that start with 0) and is greater than 2000 is \( \frac{7}{8} \) or 0.875.