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  3. [img]2015m7x/ct_egreqj_egreqjs_0095_20151[/img]From the 5 points A, B, C, D, an

[img]2015m7x/ct_egreqj_egreqjs_0095_20151[/img]From the 5 points A, B, C, D, an

游客2025-02-23  22
问题
From the 5 points A, B, C, D, and E on the number line above, 3 different points are to be randomly selected. What is the probability that the coordinates of the 3 points selected will all be positive?
选项 A、 
B、 
C、 
D、 
E、 
答案 A
解析 Of the 5 points, 3 have positive coordinates, points C, D, and E. The probability that the first point selected will have a positive coordinate is 3/5. Since the second point selected must be different from the first point, there are 4 remaining points to select from, of which 2 are points with positive coordinates. Therefore, if the coordinate of the first point selected is positive, then the probability that the second point selected will have a positive coordinate is 2/4.
Similarly, if the coordinates of the first 2 points selected are positive, then the probability that the third point selected will have a positive coordinate is 1/3.
The probability that the coordinates of the 3 points selected will all be positive is the product of the three probabilities,. The correct answer is Choice A.
Alternatively, you can compute the probability as the following fraction.
number of ways to select 3 points with positive coordinates
        number of ways to select 3 points from 5 points
Since there are only 3 points with positive coordinates, there is only 1 way to select them, so the numerator is 1. The denominator of the fraction is equal to the number of combinations of 5 objects taken 3 at a time, or "5 choose 3," which is=10. Therefore the probability is 1/10, which is Choice A.
This explanation uses the following strategy.
Strategy 12: Adapt Solutions to Related Problems
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