Question

Savita and Hamida are friends. What is the probability that both will have (i) different birthdays? (ii) the same birthday? (ignoring a leap year).

Answer 1

$\tt\it\bf\it\large\bm{\mathcal{\fcolorbox{blue}{white}{\red{Question\;1\: :-}}}}$

➠ Same birthday :-

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$\tt\it\bf\it\large\bm{\mathcal{\fcolorbox{blue}{white}{\green{Solution:-}}}}$

No. of days in an year = 365

No. of days when same birthday is

possible = 1

P(both have same birthday) =

$\frac{no.of \: days \: when \: they \: have \: same \: birthday \: in \: a \: year}{total \: no \: of \: days \: in \: a \: year}$

$= > \frac{1}{365}$

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$\tt\it\bf\it\large\bm{\mathcal{\fcolorbox{blue}{white}{\red{Question\;2\: :-}}}}$

➠ Different birthday :-

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$\tt\it\bf\it\large\bm{\mathcal{\fcolorbox{blue}{white}{\green{Solution:-}}}}$

P(of both have different birthday) = 1 -

p(of both have same birthday)

$= > 1 - \frac{1}{365}$

$= > \frac{365 - 1}{365}$

$= > \frac{364}{365}$

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