Two integers mathrm{x} and mathrm{y} are chosen with replacement from set {0,1,2,3, ldots ., 10} . T

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14.Probability

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

A

$\frac{30}{121}$

B

$\frac{62}{121}$

C

$\frac{60}{121}$

D

$\frac{31}{121}$

(JEE MAIN-2024)

Solution

$ \text { If } x=0, y=6,7,8,9,10 $

$ \text { If } x=1, y=7,8,9,10 $

$ \text { If } x=2, y=8,9,10 $

$ \text { If } x=3, y=9,10 $

$ \text { 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 $=\frac{30}{11 \times 11}=\frac{30}{121}$

Standard 11

Mathematics

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