Wednesday, June 3, 2015

When you expect 1, 1/3 the time you'll get 0...Poisson statistics

If you have a probability p of something happening, and you try 1/p times, then you have an expectation of 1 something to happen. But Poisson statistics tells you that about 1/3 the time you'll get nothing, and about 1/3 the time you'll get that 1, and about 1/3 the time you'll get more than one.

Hence if the lowest expected pregnancy rate in using a male condom is 2% in one year, and people average sexual relations 50 times in that year, 2/3 of the time the couple will find themselves pregnant, but 1/3 the time there won't be a pregnancy.  [NOTE!: The probability of 2% is given for a year, with no information on the number of sexual relations, so my assumption of an average of 50 is notional. I am quite sure that if they have no sexual relations, the likelihood of the couple finding themselves pregnant is 0%, assuming they do not have partners on the side.] The typical use pregnancy rate is 15%, which could mean that if people have sexual relations 7 times in that year, again it will be 2/3 vs. 1/3.

Put differently, you are trying to meet someone on  Say the success rate is about 1%, in that you meet someone you might consider marrying. If you meet 100 matches, again 2/3 vs. 1/3. That is, about 1/3 the time, no one will be a good match. So when people tell you that you have to keep trying and up your N, keep the failure rate in mind. If you meet 200 matches, then after those 200 meetings 13% of the time you will fail to meet a good match, and 27% you'll meet just one, and 27% you'll meet two...

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