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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.

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

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

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