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

JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Probability

Two integers x and y are chosen with replacement from the set

{0, 1, 2, 3, \dots, 10}

. Then the probability that

∣ x - y ∣ > 5

is :

Answer: (A)

Total ordered pairs

= 11 \times 11 = 121

.

For

∣ x - y ∣ > 5

: if

x = 0, y \in {6, \dots, 10}

(5 values);

x = 1

(4);

x = 2

(3);

x = 3

(2);

x = 4

(1); none for

x \geq 5

. By symmetry the same count applies with

x

and

y

interchanged.

Favourable

= 2 (5 + 4 + 3 + 2 + 1) = 30

, so the probability is

\frac{30}{121}

JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Single correct option