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Probability question

2023 · Shift 1 · Q23

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PYQ Library
JEE Advanced
Mathematics
Probability
2023 · Shift 1 · Q23

Probability question

2023 · Shift 1 · Q23

JEE AdvancedMathematicsProbabilityMCQ+3 / −1

Let

X=\left\{(x, y) \in \mathbb{Z} \times \mathbb{Z}: \frac{x^2}{8}+\frac{y^2}{20}\lt 1\right.

and

\left.y^2\lt 5 x\right\}

. Three distinct points

P, Q

and

R

are randomly chosen from

X

. Then the probability that

P, Q

and

R

form a triangle whose area is a positive integer, is :

A
$\frac{71}{220}$
B
$\frac{73}{220}$
C
$\frac{79}{220}$
D
$\frac{83}{220}$

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