JEE Main & Advanced Sample Paper JEE Main - Mock Test - 5

  • question_answer
    The probability that in a year of the 22nd century chosen at random there will be 53 Sundays is

    A) \[\frac{3}{28}\]                      

    B) \[\frac{2}{28}\]      

    C) \[\frac{7}{28}\]                      

    D) \[\frac{5}{28}\]

    Correct Answer: D

    Solution :

    We know a leap year is fallen within 4 years, so its probability \[=\frac{1}{4}\]
    \[{{53}^{rd}}\]Sunday in a leap year \[=\frac{1}{4}\times \frac{2}{7}=\frac{2}{28}\]
    Similarly probability of \[{{53}^{rd}}\] Sunday in a non-leap year  \[=\frac{3}{4}\times \frac{1}{7}=\frac{3}{28}\]
    \[\therefore \]  required probability \[=\frac{2}{28}+\frac{3}{28}=\frac{5}{28}\]


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