Probability Question 7
Question 7 - 2024 (30 Jan Shift 1)
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 :
(1) $\frac{30}{121}$
(2) $\frac{62}{121}$
(3) $\frac{60}{121}$
(4) $\frac{31}{121}$
Show Answer
Answer (1)
Solution
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 $=\frac{30}{11 \times 11}=\frac{30}{121}$
