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In the xy-plane, there are 4 points (0,0), (0,4), (6,4), and (6,0). If these 4 points makes a rectangle, what is the probability that x + y < 4 ?
A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 2/5
A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 2/5
27 Dec 2022, 04:13
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PLS CHECK THE ATTACHMENT
1/3 IS CORRECT ANS
1/3 IS CORRECT ANS
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35f4055d-b490-4e54-8c72-e33f37407e20.jpg [ 907.19 KiB | Viewed 2607 times ]
27 Dec 2022, 04:55
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We can plot the points (0,0), (0,4), (6,4), and (6,0) on the X-Y plane as shown in the figure below.
The line y = -x + 4, has its Y- intercept at (0,4), and has its X-intercept at (4,0).
The area shaded in yellow is the area of interest (y + x < 4) and we can see that a right angled triangle \(\triangle ADX\) is formed with the X-Y plane and the the rectangle ABCD.
Area of the triangle = 1/2 * base * height = \(\frac{1}{2} * 4 * 4 = 8 unit^2\)
Area of the rectangle = base * height = \(6 * 4 = 24 unit^2\)
Required Probability = 8/24 = \(\frac{1}{3}\)
Option B
The line y = -x + 4, has its Y- intercept at (0,4), and has its X-intercept at (4,0).
The area shaded in yellow is the area of interest (y + x < 4) and we can see that a right angled triangle \(\triangle ADX\) is formed with the X-Y plane and the the rectangle ABCD.
Area of the triangle = 1/2 * base * height = \(\frac{1}{2} * 4 * 4 = 8 unit^2\)
Area of the rectangle = base * height = \(6 * 4 = 24 unit^2\)
Required Probability = 8/24 = \(\frac{1}{3}\)
Option B
Attachments
Screenshot 2022-12-27 171957.jpg [ 60.67 KiB | Viewed 2528 times ]
