The probability that a year chosen at random | vedclass

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(D) century consists of $100$ years. In the $22^{nd}$ century (years $2101$ to $2200$),there are $25$ leap years and $75$ non-leap years.$1$. $A$ leap

Vedclass · Accepted Answer

$\frac{5}{28}$

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(D) century consists of $100$ years. In the $22^{nd}$ century (years $2101$ to $2200$),there are $25$ leap years and $75$ non-leap years.$1$. $A$ leap year has $366$ days,which is $52$ weeks and $2$ extra days. The probability of having $53$ Sundays in a leap year is $\frac{2}{7}$.Probability of selecting a leap year is $\frac{25}{100} = \frac{1}{4}$.So,the probability of $53$ Sundays in a leap year is $\frac{1}{4} 	imes \frac{2}{7} = \frac{2}{28}$.$2$. $A$ non-leap year has $365$ days,which is $52$ weeks and $1$ extra day. The probability of having $53$ Sundays in a non-leap year is $\frac{1}{7}$.Probability of selecting a non-leap year is $\frac{75}{100} = \frac{3}{4}$.So,the probability of $53$ Sundays in a non-leap year is $\frac{3}{4} 	imes \frac{1}{7} = \frac{3}{28}$.Total probability = $\frac{2}{28} + \frac{3}{28} = \frac{5}{28}$.

The probability that a year chosen at random from the $22^{nd}$ century will have $53$ Sundays is

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