1.

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)`

Answer» Correct Answer - 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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