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14.Probability
hard
Choose a number $n$ uniformly at random from the set $\{1,2, \ldots, 100\}$. Choose one of the first seven days of the year $2014$ at random and consider $n$ consecutive days starting from the chosen day. What is the probability that among the chosen $n$ days, the number of Sundays is different from the number of Mondays?
A
$\frac{1}{2}$
B
$\frac{2}{7}$
C
$\frac{12}{49}$
D
$\frac{43}{175}$
(KVPY-2014)
Solution
(b)
We have, $n \in\{1,2,3, \ldots, 100\}$
There are fourteen weeks in $1$ to $100$ In fourteen weeks number of Sunday is equal to number of Monday.
Only $2$ days are different number of Sundays out of $7$ days.
$\therefore$ Required probability $=\frac{2}{7}$
Standard 11
Mathematics
