Can someone please double-check my criticism of these statistics?

I'm in a discussion on another forum. Without getting too far in to it, a housemate on Big Brother had to be removed due to a medical condition which wasn't identified until a week and a half later as an ectopic pregnancy, which would have started when she had sex with another housemate in the house. There's a lot of back and forth about the credibility of this (I, personally, see no particular reason to disbelieve her as it seems unlikely and her case would have to be fairly unusual but nothing actually contradicts what's medically possible), but what I'm interested in is the following post:

Quote:

Chiming in... I work in statistics and would like to point out the following statistical facts: Assuming Kim has normal fertility, she has at most a 40% chance of pregnancy in a calendar year so for 1 cycle (month) that would be 40% divided by 12 = 3% chance Kim stated that she was using birth control. I'm going to ignore whether or not they used condoms, to make the split issue irrelevant. The worst form of birth control (diaphragm) gives you a 16% chance of pregnancy a year = 1.3% chance per month - all oral and injection methods perform much better than this. So for Kim to get pregnant with Steve the probability = 1.3% times 3.3% Overall probability of pregnancy = 0.04% Likelihood that a pregnancy is ectopic - 1 in 90 pregnancies - therefore 1.1% of pregnancies. Moreover these are significantly more likely for older mothers aged 35 or over. But lets us this percentage anyway... So Kim had a likelihood of being pregnant of 0.04%, and a 1.1% chance that that pregnancy would be ectopic. Therefore the likelihood that she was pregnant and it was ectopic is 0.04% times 1.1% Therefore the likelihood that she is telling the truth is 0.0005% To put this into context, this means that this could happen 5 times in every million times that these circumstances took place This is why I think they're lying.

Now, while I love maths, probability and statistics have always been a weak spot. Even so, this looks like a complete misapplication of probability to me. My replies have been as follows:

Quote:

What you're doing is the equivalent of rolling a 200,000-sided die, determining that the number you rolled of 35,763 has only a 1 in 200,000 chance of having come up, declaring that probability vanishingly small, and therefore concluding that the die must have been loaded.

Quote:

If you work backwards from your conclusion like that you can prove anything is vanishingly improbable. Men release between 40m and 1.2b sperm per ejaculation. Only one sperm fertilises each egg. So Kimberly's ectopic pregnancy is many orders of magnitude more likely than Kimberly actually existing in the first place. So I don't believe that Kimberly exists. If that methodology were valid, that is.

Am I right? I'm quite sure I am, but my blind spot for probability and statistics makes me want to double-check with people who are more knowledgeable than me before the conversation goes much further.

via JREF Forum http://ift.tt/1pMkCpg