QJEEM24Mab4ef: JEE Main 2024 Mathematics - Class 12 JEEM24Mab4ef Solution: Two integers and are chosen with replacement from the set .…

Question

Verified Solution • 2025–26 Session moderate

Two integers $x$ and $y$ are chosen with replacement from the set $\{0,1,2,3, \ldots, 10\}$ . Then the probability that $|x-y|>5$ , is :

Accepted Answer

If $x=0, y=6,7,8,9,10$

If $x=1, y=7,8,9,10$

If $x=2, y=8,9,10$

If $x=3, y=9,10$

If $x=4, y=10$

If $x=5, y=$ no possible value

Total possible ways $=(5+4+3+2+1) \times 2$

$=30$

Required probability $=\frac{30}{11 \times 11}=\frac{30}{121}$

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