Answer:
To find the probability of numbers lying between 500 and 900 inclusive with exactly two consecutive figures that are identical, we can use the following steps: Step 1: Count the total number of three-digit numbers between 500 and 900 inclusive. There are 400 three-digit numbers between 500 and 900 inclusive. Step 2: Count the number of three-digit numbers between 500 and 900 that have exactly two consecutive figures that are identical. We can break this down into cases based on the middle digit of the three-digit number. Case 1: The middle digit is not 0 or 9. In this case, there are 8 possible digits that can be used for the middle digit (i.e., 1, 2, 3, 4, 5, 6, 7, or 8). For each possible middle digit, there are