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Question
The probability that in a year of 22nd century chosen at random, there will be 53 Sunday, is ______.
Options
3/28
2/28
7/28
5/28
None of the
Solution
The probability that in a year of 22nd century chosen at random, there will be 53 Sunday, is `underlinebb(5/28)`.
Explanation:
We know, a leap year is fallen within 4 years, so probability `= 25/100 = 1/4`
In a century, the probability of 53 Sundays in a leap year = `1/4 xx 2/7 = 2/28`
Non-leap year in a century = 75
Probability of selecting a non-leap year `= 75/100 = 3/4`
Probability of 53 Sundays in a non-leap year = `1/7`
Similarly, in a century, the probability of 53 Sundays in a non-leap year = `3/4 xx 1/7 = 3/28`
∴ Required Probability = `2/28 + 3/28 = 5/28`
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