In an assembly of 4 persons the probability that atleast 2 of them have the same birthday, is

Options

A. `0.293`
B. `0.24`
C. `0.0001`
D. `0.016`

Answer

D

Explanation

Required probability = P (two persons have same birthday)
+ P (three persons have same birthday)
+ P (four persons have same birthday)
`= .^(4)C_(2)xx(1)/(365)xx((364)/(365))^(2)+ .^(4)C_(3)(1)/((365)^(2))xx(364)/(365)+ .^(4)C_(4)((1)/(365))^(3)`
`= (6(364)^(2)+4xx364+1)/((365)^(3))=(794976 + 1456+1)/((365)^(3))`
`= (796433)/(48627125)=0.016`