Question

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

• A. $\frac{7}{11}$
• B. $\frac{40}{121}$
• C. $\frac{35}{121}$
• D. $\frac{30}{121}$

Answer 1

The correct option is D $\frac{30}{121}$

Since x and y can take values from 0 to 10. So, the total number of ways of selecting x and y is $11\times 11=121$
Now, |x - y| > 5 $\Rightarrow$ x - y < - 5 or x - y > 5
There are 30 pairs of values of x and y satisfying these two inequalities, so favourable number of ways = 30
Hence, required probability = $\frac{30}{121}$