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Question

The probability that a leap year selected at random will contain either 53 thursdays or 53 fridays is:

A
5/7
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B
4/7
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C
3/7
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D
2/7
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Solution

The correct option is C 3/7A leap year contains 366 days. If the first day of the leap year is a Monday, then Monday and Tuesday will occur 53 times and Wednesday, Thursday, Friday, Saturday, and Sunday will each occur 52 times. So there are 7 possible cases: Leap year starts on a Monday, result: 53 Mondays and 53 Tuesdays. Leap year starts on Tuesday: 53 Tuesdays and 53 Wednesdays. Leap yr. begins Wednesday: 53 Wednesdays and 53 Thursdays. Leap yr. begins Thurs.: 53 Thursdays and 53 Fridays Leap year begins Fri.: 53 Fridays and 53 Saturdays Leap year begins Sat.: 53 Saturdays and 53 Sundays Leap year begins Sun.: 53 Sundays and 53 Mondays. So, 3 possibilities of having 53 thursdays or 53 fridays p(53 thursdays or 53 fridays in leap year) = 37

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