Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Since x and y each 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
When
x - y > 5, we have following cases:
$\begin{array}{ccc}ValueofX& Valueofy& Numberofcases\\ 6& 0& 1\\ 7& 0,1& 2\\ 8& 0,1,2& 3\\ 9& 0,1,2,3& 4\\ 10& 0,1,2,3,4& 5\\ & Totalnumberofcases& 15\end{array}$
Similarly, we have 15 cases for x – y < 5. There are 30 pairs values of x and y satisfying these two inequalities. So, favorable number of ways is 30. Hence, required probability is $\frac{30}{121}$