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I'm given this problem:

Consider there are two applicants for a job. One of the applicants is a man, and it is known that he was born on a Wednesday. What is the probability that a second applicant is also a man?

I don't get the question. It seems that being a man for two applicants is independent regardless of the birthday or gender of the first applicant. Moreover, when there is no data, how can I calculate a probability!

Please guide me on how can I answer this question or similar ones.


marked as duplicate by JMoravitz, John Douma, Xander Henderson, Lord Shark the Unknown, Leucippus Mar 11 at 4:01

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    $\begingroup$ This is a rephrasing of one of the variants of the boy-girl paradox. Before continuing, it must be made absolutely and unambiguously clear what is being asked. One of the most common intended interpretations is the following: We have two applicants, we'll call them $A$ and $B$ for now. The person conducting the interviews gets to meet both and notes their gender and asks them what day of the week each was born... $\endgroup$ – JMoravitz Mar 10 at 22:04
  • $\begingroup$ Now... we haven't yet met either but we go to the interviewer and ask them the very specific yes/no question "is at least one of the applicants a man born on a wednesday?" to which the interviewer responds "yes." Armed with this knowledge what is the probability from our perspective that both are men? The solution will rely on calculations of conditional probabilities and Bayes' theorem. $\endgroup$ – JMoravitz Mar 10 at 22:04
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    $\begingroup$ If the intended interpretation is anything other than what I outlined above, for example if the interviewer offers us this information without being asked, then we need more information as to the thought process of the interviewer. The interviewer might just be telling us the gender and day of week of the first interviewer every time regardless of what the genders/days were, at which point the probability would simply be $\frac{1}{2}$ (assuming genders are equally distributed, another common assumption for the problem). $\endgroup$ – JMoravitz Mar 10 at 22:07
  • $\begingroup$ @JMoravitz Thank you! $\endgroup$ – Ahmad Mar 11 at 9:34