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25 Sep 2024, 07:37
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
36% (00:50) correct
63% (00:45) wrong based on 11 sessions
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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?
A. 1/10
B. 1/5
C. 3/10
D. 2/5
E. 3/5
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27 Oct 2024, 02:48
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OE
Of the 5 points, 3 have positive coordinates, points C, D, and E. The probability that the frst point selected will have a positive coordinate is 3/5. Since the second point selected must be different from the frst point, there are 4 remaining points to select from, of which 2 are points with positive coordinates. Therefore, if the coordinate of the frst 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 frst 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, (3/5)(2/4)(1/3), or 1/10. The correct answer is Choice A.
Of the 5 points, 3 have positive coordinates, points C, D, and E. The probability that the frst point selected will have a positive coordinate is 3/5. Since the second point selected must be different from the frst point, there are 4 remaining points to select from, of which 2 are points with positive coordinates. Therefore, if the coordinate of the frst 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 frst 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, (3/5)(2/4)(1/3), or 1/10. The correct answer is Choice A.
