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Consider the set X = {(x, y) ∈ Z × Z: x²/8 + y²/220 < 1 and y² < 5x}. If three distinct points P, Q, and R are selected randomly from X, what is the probability that these points form a triangle with an area that is a positive integer?
- 71/220
- 73/220
- 79/220
- 83/220
Correct answer: 73/220
Solution
The points in set X are constrained by the given inequalities, and the probability of forming a triangle with a positive integer area is calculated by considering all valid combinations of points. The result simplifies to 73/220.
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