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प्रश्न
Find the probability that in a leap year there will be 53 Tuesdays ?
उत्तर
GIVEN: A leap year
TO FIND: Probability that a leap year has 53 Tuesdays.
Total number of days in a leap year is 366 days.
Hence number of weeks in a leap year is`366/7 =52 Weeks and 2 day `
In a leap year we have 52 complete weeks and 2 day which can be any pair of the day of the week i.e.
(SUNDAY, MONDAY)
(MONDAY, TUESDAY)
(TUESDAY, WEDNESDAY)
(WEDNESDAY, THURSDAY)
(THURSDAY, FRIDAY)
(FRIDAY, SATURDAY)
(SATURDAY, SUNDAY)
Let A be the event that a leap year has 53 Tuesdays.
The event A will occur if the last two days of the leap year are either Monday and Tuesday or Tuesday and Wednesday.
Therefore, Favourable number of elementary events = 2
Hence total number of pairs of days is 7.
We know that Probability = `'\text{Numbers of favourable event} /\text{total numbers of event}'`
Hence probability that a leap year has 53 Tuesdays =
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