Question

What is the probability of getting 53 Sundays in
a) a leap year
b) a non- leap year.

please I need the answer in proper step and well explained​

Answer 1

Probability of getting 53 Sundays in

a) A leap year   -  $\bf{\dfrac{2}{7}}$

b) A non- leap year -  $\bf{\dfrac{1}{7}}$

Step-by-step explanation:

• Part-A For a Leap year

a) A year = 365 days,

While the leap year has 366 days.

A leap year has 52 week which can be shown as:

Leap year =52 weeks x 7 days = 364 days and 2 days left

The remaining 2 days could could be in pair like:

Sunday, Monday

Monday, Tuesday,

Tuesday, Wednesday

Wednesday, Thursday

Thursday, Friday

Friday, Saturday

Saturday, Sunday

As above mentioned 7 days pair, we have 2 pairs only which is having Sunday.

so the probability of getting 53 Sunday =   $\bf{\dfrac {2}{7}}$

• Part- B For non Leap year

b) For non leap year we have, 1 year = 365 days

so we can write it as:

1 year = 52 weeks x 7 days = 364 days and 1 day left

The remaining day could be as:

Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday

There is only 1 day left, if the day is not Sunday,

The probability of getting 52 Sundays = $\dfrac{6}{7}$

The probability of getting 53 Sunday = $1 -\dfrac{6}{7} = \dfrac{1}{7}$

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Answer 2

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In a non-leap year there will be 52 Sundays and 1 day will be left. This 1 day can be Sunday, Monday, Tuesday, Wednesday, Thursday, friday , Saturday, Sunday. Of these total 7 outcomes, the favourable outcomes are 1. Hence the probability of getting 53 sundays = 1 / 7.❤️