Question

Find the probability of 53 Sundays in a year selected at random

Answer 1

it depends whether its leap year or normal year
if its normal then it will have 365 days and it means 1 extra day when you divide it with 7 so that day can be anything
so the probability of it being Sunday is 1/7
if its leap year then you have 2 extra days and Sunday can be on any day so the probability will be 2/7

Answer 2

Answer:

In a leap year there are 366 days. In 366 days, we have 522 weeks and 2 days, Thus we can say that leap year ah always 52 Sundays.

The remaining two days can be

(i) Sunday and Mondays

(ii) Mondays and Tuesdays

(iii) Tuesday and Wednesday

(iv) Wednesday and Thursday

(v) Thursday and Friday

(VI) Friday and Saturday

(vii) Saturady and Sunday.

From above it is clear that there are 7 elementary events associated with this random experiment.

Clearly the event A will happen if the last two days of the leap year are either Sunday and Monday or Saturday and Sunday.

∴ P (E) = n (E)/n (S) = 2/7