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STD 11 - 14. probability — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 14. probability4 Marks
MCQ
The probability that a leap year selected randomly will have $53$ Sundays is
  • A
    $\frac{1}{7}$
  • ✓
    $\frac{2}{7}$
  • C
    $\frac{4}{{53}}$
  • D
    $\frac{4}{{49}}$
✓

Answer

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

Hence required probability $ = \frac{2}{7}.$

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