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Roll numbers given to a select of students are unique 4 digit numbers. One roll number is picked up at random, what is the probability that the chosen number is divisible by 11 or 13 ?
  • a)
    1/6
  • b)
    161/1000
  • c)
    289/1799
  • d)
    289/1800
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Roll numbers given to a select of students are unique 4 digit numbers....
In the question. We have to count 4 digit numbers which are multiples of 11, 13 and 143 (product of 11 and 13).
The first 4 digit multiple of 11, 13 as well as 143 is 1001 = 11×91= 13×77= 143×7
The last 4 digit multiple of 11 is 9999 =11×909 and that of 13 is 9997 =13×769 and for 143 is 9867 (=143×69)
Number of 4 digit multiple of 11, 13 and 143 are (909-91+1), (769-77+1) and (69-7+1)
i.e. 819,693 and 63 respectively.
The number of 4 digit roll numbers which are divisible by 11 and 13 are 819+693-63=1449 Number of 4 digit numbers are from 1000 to 9999 i.e. 9000.
Probability of selection the required roll number = 
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Roll numbers given to a select of students are unique 4 digit numbers. One roll number is picked up at random, what is the probability that the chosen number is divisible by 11 or 13 ?a)1/6b)161/1000c)289/1799d)289/1800Correct answer is option 'B'. Can you explain this answer?
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