Q262 / 270 · NDA 2012 (Phase 2) · Mathematics

What is the probability that a leap year selected at random will contain 53 Mondays?

  • Correct answer
    A
    $\frac{2}{5}$
  • B
    $\frac{2}{7}$
  • C
    $\frac{1}{7}$
  • D
    $\frac{5}{7}$

Solution

A leap year contain 366 days i.e., 52 weeks and 2 days, clearly there are 52 Mondays in 52 weeks. For the remaining two days, we may have any of the following two days. (i) Monday and Tuesday (ii) Tuesday and Wednesday iii) Wednesday and Thursday iv) Thursday and Friday (v) Friday and Saturday vi) Saturday and Sunday sii) Sunday and Monday Now for 53 Mondays, one of the two days must be Monday. Hence, the required probability $=\frac{2}{7}$.

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

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