Two integers x and y are chosen with replacement from the set {0, 1, 2, 3,…,10}. Then the probability that is

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Solution

Q.
Two integers $x$ and $y$ are chosen with replacement from the set {0, 1, 2, 3,…,10}. Then the probability that $| x - y | > 5,$ is [2024]

1 $\frac{60}{121}$

2 $\frac{31}{121}$

3 $\frac{62}{121}$

4 $\frac{30}{121}$

Ans.
(4)

Let $E = {(x, y) : | x - y | > 5}$ and $x, y \in {0, 1, 2, \dots, 10}$

$∴$ $E = {(0, 6), (0, 7), (0, 8), (0, 9), (0, 10), (1, 7), (1, 8), (1, 9), (1, 10), (2, 8), (2, 9), (2, 10), (3, 9), (3, 10), (4, 10),$ $(6, 0), (7, 0), (8, 0), (9, 0), (10, 0), (7, 1), (8, 1), (9, 1), (10, 1), (8, 2), (9, 2), (10, 2), (9, 3), (10, 3), (10, 4)}$

$∴$ $n (E) = 30$

Total number of possible outcomes $= 11 \times 11 = 121$

$∴$ $Required probability = \frac{30}{121}$

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