Q77 / 160 · TS EAMCET 2020 (11 Sep Shift 2) · Mathematics

4-digit numbers are formed using the digits $4,5,6,7,8,9$ allowing repetition of the given digits. If a number is chosen at random from those numbers thus formed, then the probability that it is exactly divisible by 3 is

  • A
    $\frac{7}{36}$
  • B
    $\frac{5}{18}$
  • C
    $\frac{5}{6}$
  • Correct answer
    D
    $\frac{1}{3}$

Solution

If we form a 4-digit number by using the digits 4, 5, 6, 7, 8, 9 allowing repetition, then we can categories the remainders on dividing by 3 as 0,1 or 2 , so the probability to form a number which is exactly divisible by 3 is $\frac{1}{3}$.

Hence, the correct answer is option: 'D'.

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