#### Question

# what is the probability that a leap year, selected as random, will contain 53 sundays?

ts a math question of classs 12

#### Answer

1/7?

Maybe 1/7 because there are 7 days in a week?

eeeh, wrong. 52ƫ=364 so if a year is 364 days long there are 52 Sundays. For a 365 day year (normal year), if the year starts on a Sunday, it will end on a Sunday and the probability of 53 Sundays is 1/7. For a 366 day year (leap year). If the year starts on Saturday, it will end on Sunday (giving 53 Sundays), however if it starts on Sunday, it will end on Sunday (another combination giving 53 Sundays). If a leap year starts on any other day there will only be 52 Sundays. selecting a leap year at random, I presume, is telling you that the day of the week a year starts on it a uniform distribution across the days of the week. There are two chance, out of seven, that yields 53 Sundays. Answer 2/7.

PS - there appears to be a formatting problems with this web site. 52ƫ=364 is fifty two times seven equals 364.