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Find the probability of 53 Sundays and 5...

Find the probability of 53 Sundays and 53 Mondays in a leap year.

A

`(2)/(7)`

B

`(4)/(7)`

C

`(3)/(7)`

D

`(1)/(7)`

Text Solution

Verified by Experts

The correct Answer is:
C
A leap year consists of 366 days comprising of 52 weeks and 2 days. There are 7 possibilities for these 2 extra days viz., (i) Sunday, Monday (ii) Monday, Tuesday (iii) Tuesday, Wednesday (iv) Wednesday, Thursday (v) Thursday, Friday (vi) Friday, Saturday (vii) Saturday, Sunday.
Let us consider two events :
A : The leap year contains 53 Sundays
B : The leap year contains 53 Mondays.
We have,
`P(A)=(2)/(7),P(B)=(2)/(7), P(A cap B)=(1)/(7)`
Required probability
`=P(A cup B)`
`= P(A)+P(B)-P(A cap B)=(2)/(7)+(2)/(7)-(1)/(7)=(3)/(7)`
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