Question

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

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

Answer 1

Answer: (D)

Required probability $=P($ When two persons have same birthday) $+P$ (When three persons have same birthday) $+P$ (When four persons have same birthday)
$={}^4{C}_2\times \frac{1}{365}\times {\left(\frac{364}{365}\right)}^2+{}^4{C}_3\frac{1}{(365{)}^2}\times \frac{364}{365}$
$+{}^4{C}_4{\left(\frac{1}{365}\right)}^3$
$=\frac{6(364{)}^2+4\times 364+1}{(365{)}^3}$
$=\frac{794976+1456+1}{(365{)}^3}$
$=\frac{796433}{48627125}$
$=0.016$