Interview Question: Beating the Odds

Sample Question #174 (probability theory)

Aidan is a Ph.D. in statistics who likes to have unprotected sex with his girlfriend Brittany. He knows that, on average, there’s a 1 in 6 chance that a woman who’s not on the pill could get pregnant from unprotected sex in any given month. After 9 months, what’s the probability that Brittany will still not be pregnant?

(Comment: while this is a good probability question, the way it’s presented — all that context about "unprotected sex" — could well make you feel uncomfortable. If you do feel this way, you should make a note of it and consider reporting the question as inappropriate to the head of the hiring group, the company recruiter or the headhunter later, after the interview is over. I phrased this question exactly because there are (male) interviewers who like to pepper their otherwise quantitative questions with allusions to sex.)

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One Response to Interview Question: Beating the Odds

  1. Brett says:

    ANSWER
     
    There are nine events and they’re independent of each other. The expected probability of not getting pregnant in a month is 5/6, therefore the expected probability of Brittany’s staying unpregnant after nine months is (5/6)^9.
     

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