Question

What s the chance that (i) non-leap year (ii) leap year should have fifty three Sundays?

Answer 1

(i) I a non-leap year there are 365 days (52 works +1 day).

In 52 weeks we will have 52 Sundays and the one remaining day can be any from the following.

1. Sunday

2. Monday

3. Tuesday

4. Wednesday

5.Thursday

6.Friday

7. Saturday

So, the probability of getting 53 Sundays in a non-leap year is 1/7.

(ii) In a leap year we have 366 days (52 weeks +2 days).

The remaining 2 days may be of order.

1. Sunday and Monday

2. Monday and Tuesday

3. Tuesday and Wednesday

4. Wednesday and Thursday

5. Thursday and Friday

6. Friday and Saturday

7. Saturday and Sunday.

Only the above order will be followed for the renaming 2 days (366-364) of leap year.

In the order we will get 2 Sunday out of 7 probabilities, so the answer is 2 out of 7.

So, the probability of leap year should have 53 Sundays

= 2/7.