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[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
35
管理
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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