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 :

Step-by-step solution

Given set is 0 , 1 , 2 , 3 , . . . , 10 . So, total number of outcomes are 11 × 11 = 121 Favourable outcomes are: 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 And the same number of elements when x and y are interchanged. So, the number of favourable outcomes are 30 . So, the required probability is given by P E = 30 121 .