# Why Probaility that two guys are born in same month is 1/12 but not 1/2.

Assuming that it is equally like to be born in any of the 12 months.

Reasoning for 1/2: Probability that both are born in the month of Jan is 1/12*1/12 as event must happen one after another. This probability is same for every other month. The event can happen in any of the 12 months, we need to add 1/24, 12 times. So we got 1/2.

Reasoning for 1/12: There are 144 total outcomes and 12 favorable outcome. All the event are equally likely so the probability is 1/12.

Where am I doing wrong? Please suggest.

• For the first one, it should be $1/144$ $12$ times. – Alex S Sep 27 '15 at 4:46
• I don't understand. Is that $\frac{1}{12} \times \frac{1}{12}= \frac{1}{24}$? ;) – Asydot Sep 27 '15 at 4:46
• $$\frac{1}{12}\times\frac{1}{12}=\frac{1}{12\times 12}=\frac{1}{144}$$ $$\underbrace{\frac{1}{144}+\frac{1}{144}+\cdots+\frac{1}{144}}_{\text{12 times}}=12\times\frac{1}{144}=\frac{1}{12}$$ – Zev Chonoles Sep 27 '15 at 4:46
• :-( My bad... Thanks guys – Deepak Sep 27 '15 at 4:48

$\frac1{12} \times \frac1{12}$ is not $\frac1{24}$.