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The probability that an year chosen at r...

The probability that an year chosen at random has 53 Sundays is :

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A normal year has 52 Sundays, 52 Mondays, 52 Tuesday, 52 Wednesday, 52 Thursday, 52 Fridays, 52 Saturdays, +1 day that could be anything depending upon the year consideration.
For a leap year to have 35 Sundays, it should start from Saturday or Sunday.
So, basically we have to find the probability that year start from Saturday or Sunday (P)
`P=frac{text { first day to be Saturday or Sunday }}{{ T otal no. of days in a week }}`
...
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