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# If a leap year is selected at random, what is the chance that it will contain 53 Tuesdays?

Tutor

No of days in leap year = 366 No of weeks =366/7= 52 and 2days 2 days will come 53 times in a leap year. No of days in a week = 7 Probability of ( Tuesday 53 times in a leap year)= 2/7

Teacher

There are 52 weeks in a leap year + 2 days. These 2 days can be (MT)(TW)(WTh)(ThF)(FS)(SS). Thus, there are two chances of having tuesday. Hence, the probability is 2/7

In a leap year, there are 366 days i.e., 52 weeks and 2 days. In 52 weeks, there are 52 Tuesdays. Therefore, the probability that the leap year will contain 53 Tuesdays is equal to the probability that the remaining 2 days will be Tuesdays. The remaining 2 days can be Monday and Tuesday Tuesday and Wednesday Wednesday...

In a leap year, there are 366 days i.e., 52 weeks and 2 days.

In 52 weeks, there are 52 Tuesdays.

Therefore, the probability that the leap year will contain 53 Tuesdays is equal to the probability that the remaining 2 days will be Tuesdays.

The remaining 2 days can be

Monday and Tuesday

Tuesday and Wednesday

Wednesday and Thursday

Thursday and Friday

Friday and Saturday

Saturday and Sunday

Sunday and Monday

Total number of cases = 7

Favourable cases = 2

∴Probability that a leap year will have 53 Tuesdays =

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