Question Number 182952 by mr W last updated on 17/Dec/22
$${what}\:{is}\:{the}\:{probability}\:{that}\:{at}\:{least} \\ $$$${two}\:{from}\:\mathrm{23}\:{people}\:{have}\:{birthday}\:{at} \\ $$$${the}\:{same}\:{day}? \\ $$$$ \\ $$$$\left({an}\:{unsolved}\:{old}\:{question}\right) \\ $$
Answered by aleks041103 last updated on 17/Dec/22
$${we}\:{want}\:{p}. \\ $$$$\mathrm{1}−{p}\:{is}\:{the}\:{probability}\:{all}\:\mathrm{23}\:{people}\:{have}\:{different} \\ $$$${birthdays}. \\ $$$$\Rightarrow\mathrm{1}−{p}=\frac{\mathrm{365}.\mathrm{364}.\mathrm{363}…\mathrm{343}}{\mathrm{365}.\mathrm{365}.\mathrm{365}…\mathrm{365}}\approx\mathrm{0}.\mathrm{4927} \\ $$$$\Rightarrow{p}\approx\mathrm{50}.\mathrm{7\%} \\ $$
Commented by mr W last updated on 17/Dec/22
$${yes}.\:{thanks}\:{sir}! \\ $$