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Three numbers are chosen at random without replacement from 1,2,....10 . The probability that the minimum of the chosen numbers is 3, or their maximum is 7 is ..............

A. 7/24
B. 11/40
C. 17/60
D. 1/4

User Yuri
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1 Answer

3 votes

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.

User DatsunBing
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