The probability that the sum of the x-coordinate and the y-coordinate of the chosen lattice point will be odd is 7/15. The correct answer is 7/15.
The image shows a rectangle with vertices at (0,0), (6,0), (6,4), and (0,4). The lattice points inside the rectangle are:
(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3), (4,1), (4,2), (4,3), (5,1), (5,2), (5,3)
There are 15 lattice points inside the rectangle.
Of these, 7 have an odd sum:
(1,1), (1,3), (2,1), (2,3), (3,1), (3,3), (5,1).
Therefore, the probability that the sum of the x-coordinate and the y-coordinate of the chosen lattice point will be odd is 7/15.
The correct answer is 7/15.
Question
A Rectangle, with its vertex coordinates labeled, s graphed in the standard coordinate plane below. A lattice point is a point with coordinates that are both integers. A lattice point inside but not on the rectangle will be chosen at random. What is the probability that the sum of the x-coordinate d the y coordinate of the chose lattice point will be odd?
- 1/5
- 2/5
- 7/15
- 17/35
- 1/2