Final answer:
The probability that two different randomly chosen numbers from the set (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) are no greater than 10 is approximately 0.2441.
Step-by-step explanation:
To find the probability that two different randomly chosen numbers from the set (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) are no greater than 10, we need to find the number of favorable outcomes divided by the total number of possible outcomes.
In this case, the favorable outcomes are all pairs of numbers that are no greater than 10. There are 11 pairs in total: (0,0), (0,1), (0,2), ..., (9,9). The total number of possible outcomes is the number of ways to choose 2 numbers out of 10, which can be calculated using the combinations formula: nCr = n! / (r!(n-r)!). In this case, n = 10 and r = 2.
Using the formula, we can calculate: nCr = 10! / (2!(10-2)!) = 10! / (2!8!) = (10 * 9) / (2 * 1) = 45.
Therefore, the probability is: favorable outcomes / total outcomes = 11 / 45 ≈ 0.2444.
So, the correct answer is 0.2441.