Final answer:
To find the probability that the minimum of the chosen numbers is 3 or their maximum is 7, we calculate the individual probabilities and add them together. The probability that the minimum is 3 is 9/36, and the probability that the maximum is 7 is 6/15. Adding these probabilities gives us 7/24. So the correct answer is Option A.
Step-by-step explanation:
To solve this problem, we need to calculate the probability that the minimum of the chosen numbers is 3 and the probability that their maximum is 7, and then add these probabilities together.
1. Probability that the minimum is 3:
The minimum number must be 3, and the other two numbers can be chosen from the remaining 1, 2, 4, 5, 6, 7, 8, 9, 10. There are 9 possible choices for each of the remaining two numbers. So, the probability is 9/9C2 = 9/36.
2. Probability that the maximum is 7:
The maximum number must be 7, and the other two numbers can be chosen from the remaining 1, 2, 3, 4, 5, 6. There are 6 possible choices for each of the remaining two numbers. So, the probability is 6/6C2 = 6/15.
Adding these probabilities together, we get 9/36 + 6/15 = 7/24. Therefore, the answer is Option A: 7/24.