Probability
Discrete Uniform — Probability of |x−y| > 5
nta_pyq_2024_jan
Grade 12
Question:
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:
$\dfrac{30}{121}$
$\dfrac{62}{121}$
$\dfrac{60}{121}$
$\dfrac{31}{121}$
Step-by-Step Solution
Key Concept: Count ordered pairs $(x,y)$ from $\{0,\ldots,10\}^2$ with $|x-y|>5$, i.e., $y-x>5$ or $x-y>5$.
30 ordered pairs with $|x-y|>5$. $P=30/121$.
Correct Answer: 1