Poll of the Day > Condoms only working 97% of the time seems like a low ball

(+) Yeah! (+)

That would mean after 98th time of having sex, you are prego
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That's not how that works, I hope you know.

Actually, the event you're describing can be modeled using a geometric distribution.

So the probability of getting pregnant after the 98th time would be f(98) = (0.03)(0.97)^(97) = 0.16%, which is pretty damn low.
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shadowsword87 posted...

That's not how that works, I hope you know.

well percentage changed into a fraction would be 97/100, which as odds would be 97 out of 100 times

so 3 of the 100 times it doesnt work. Its all simple math
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EclairReturns posted...

Actually, the event you're describing can be modeled using a geometric distribution.

So the probability of getting pregnant after the 98th time would be f(98) = (0.03)(0.97)^(97) = 0.16%, which is pretty damn low.

Isn't that equation also assuming that without a condom, sex would lead to pregnancy 100% of the time? Which should be another factor that lowers the odds, since it is much lower than 100%.
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The Popo posted...

Isn't that equation also assuming that without a condom, sex would lead to pregnancy 100% of the time?

Is it? All I know is that the geometric distribution models TC's scenario with the parameters: n = 98, p = 0.03 for f(x) = [p^x] [(1-p)^(n-x)]. Correction: the function was f(1), not f(98).
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EclairReturns posted...

The Popo posted...

Isn't that equation also assuming that without a condom, sex would lead to pregnancy 100% of the time?

Is it? All I know is that the geometric distribution models TC's scenario with the parameters: n = 98, p = 0.03.

Well, I could be wrong here, but the success rate of a working condom would presumably be how often it prevents a fluid transfer, and not how often it prevents a pregnancy. The math equation should be correct, but we would also need to know how often unprotected sex leads to pregnancy in order to take it one step further.

That's my take on it, at least. If anyone thinks I'm wrong on this, by all means, correct me.
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wwinterj25 posted...

Okay, so one of them is immortal by math logic.
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Not true.

https://www.youtube.com/watch?v=Z4dO_K_DufQ
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EclairReturns posted...

Actually, the event you're describing can be modeled using a geometric distribution.

So the probability of getting pregnant after the 98th time would be f(98) = (0.03)(0.97)^(97) = 0.16%, which is pretty damn low.

I was curious so wrote a quick some quick and dirty code that generates a random number (the languages built in random seed isn't perfectly random, but it's close enough for our purposes) 1-100 10 million times where 3 of the numbers (representing a failure and a failure rate of 3 in 100) increment a counter. After the 10 million iterations I determine what percentage of the 10 million random numbers landed on one of the three failures. The result every time I run it is approximately 3%.

I'm terrible at probability, but do you have any idea why that would be? Is there something inherently wrong with my test methodology?

EclairReturns posted...

Okay, so one of them is immortal by math logic.

Sounds legit.
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ectopants posted...

Not true.

https://www.youtube.com/watch?v=Z4dO_K_DufQ

Very informative
That makes more sense how they got that number now, thank you
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Duck-I-Says posted...

generates a random number (the languages built in random seed isn't perfectly random, but it's close enough for our purposes) 1-100 10 million times

Well, to be honest, I'm just using stuff from the probability class I'm taking this semester. In this case, the experiment (sex) is repeated 97 times until a condom failure occurs on the 98th try. Whereas your code repeats it many more times, and doesn't stop the experiment even after a condom failure has already occurred. The probabilistic equivalent to this would be the binomial distribution, I think.
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EclairReturns posted...

Well, to be honest, I'm just using stuff from the probability class I'm taking this semester. In this case, the experiment (sex) is repeated 97 times until a condom failure occurs on the 98th try. Whereas your code repeats it many more times, and doesn't stop the experiment even after a condom failure has already occurred. The probabilistic equivalent to this would be the binomial distribution, I think.

Ohhhhh that makes a lot more sense. Yeah I totally misinterpreted what you were saying and thought you were somehow implying a 3% failure rate meant a 0.16% chance of failing in 100 tries, not the chance that it occurs on exactly the 98th try. Thanks for the clarification.

An effective contraceptive is to jam a cotton bud/swab down your urethra, and leave it there for the duration!
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Condoms probably break more then 2% of the time, but, if you notice it and get a new one, then there is very little risk of pregnancy (not going to go into specifics here as to why there is a chance at all).

Also probably depends on other factors how often they break etc.

Also, just simple logical timing, in addition to using a condom can drastically reduce the chance of pregnancy even more.

If you combine a condom with pulling out and timing method, I would imagine the chance is extremely low.
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Y'all do know that if you have sex without a condom, it's not like there's a 100% sucsess rate at becoming pregnant, right?

Birth control success rates are given on a per person per year basis, which is a really weird and rather uninformative way to do it. It doesn't actually take into account frequency of sex beyond some average number, which is widely variable and a major factor that needs to be considered.

Also, condoms are more like 85% with typical use. 97% is with perfect use, which means no breakage, no slippage, and no deterioration, and that last one in particular is impossible to completely prevent unless you're inspecting the whole thing with a microscope before use (at which point you've unrolled it and it's going to be hard to get on properly anyway). Condoms on their own aren't a great birth control method.

wolfy42 posted...

Condoms probably break more then 2% of the time,

If properly used, breakage rate is about 0.4% (though obviously that's an average derived from a few different styles, since thinner ones will be more fragile). If you're seeing more than that, you may be doing something wrong.
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I don't know if I'm interpreting the probability wrong, but it seems to me as if you kept using a condom until you accidentally got pregnant, on average you would get pregnant on the 34th time you had sex. However, I also calculated the variance to be like 1078 which seems weird to me.

Also, another thing is that the most common thing would be for condom failure to occur on the very first time. The geometric distribution is sort of weird.
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jramirez23 posted...

I don't know if I'm interpreting the probability wrong, but it seems to me as if you kept using a condom until you accidentally got pregnant, on average you would get pregnant on the 34th time you had sex. However, I also calculated the variance to be like 1078 which seems weird to me.

Also, another thing is that the most common thing would be for condom failure to occur on the very first time. The geometric distribution is sort of weird.

That's accurate I think. Basically if the failure occurs on the first time, those people are taken out of the sample population, so progressive runs have fewer and fewer people and so fewer failures. The average is 34, but you can also have people who take 100 or more times to fail so that skews the variance.

adjl posted...

Also, condoms are more like 85% with typical use. 97% is with perfect use, which means no breakage, no slippage, and no deterioration, and that last one in particular is impossible to completely prevent unless you're inspecting the whole thing with a microscope before use (at which point you've unrolled it and it's going to be hard to get on properly anyway). Condoms on their own aren't a great birth control method.

Way to fucking scare me, adjl. We're not even into October yet.
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Zeus posted...

adjl posted...

Also, condoms are more like 85% with typical use. 97% is with perfect use, which means no breakage, no slippage, and no deterioration, and that last one in particular is impossible to completely prevent unless you're inspecting the whole thing with a microscope before use (at which point you've unrolled it and it's going to be hard to get on properly anyway). Condoms on their own aren't a great birth control method.

Way to fucking scare me, adjl. We're not even into October yet.

It's true. Relying exclusively on condoms isn't a good idea at all. You can get that number quite a bit higher by relying on other methods, including normally-weak ones like pulling out and the rhythm method, but condoms alone? Not so good.
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I don't know if it means anything but I fill the condoms with water after sex to see if there are any leaks.
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EclairReturns posted...

Actually, the event you're describing can be modeled using a geometric distribution.

So the probability of getting pregnant after the 98th time would be f(98) = (0.03)(0.97)^(97) = 0.16%, which is pretty damn low.

...what?

If there is a 97% chance of success with each use of a condom, that means there is a 3% chance of failure with one use. That overall chance of failure will increase with each use.

You're saying that you're less likely to get someone pregnant by having sex 98 times (0.16%) than by having sex once (3%). This doesn't make any sense. You didn't need to multiply by an initial value of 0.03.

The probability of success can be expressed by: 0.97^n, where n is the number of times.

0.97^98 = 0.05 or 5% chance of never once having a condom break. Or in other words a 95% chance of failure.

This is assuming however that the 97% statistic is true, but it's also not recognizing that a condom failure doesn't mean a pregnancy.
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Can't you just hose out the vagina and that would flush out any stray swimmers?

adjl posted...

Also, condoms are more like 85% with typical use. 97% is with perfect use

Pretty sure the percentage are based off of a years worth of use to the person with the average sex life, not every individual time having sex.

So like with perfect use there is only 3% chance of pregnancy over the course of an entire year, and like 15% chance with typical use over an entire year
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madadude posted...

adjl posted...

Also, condoms are more like 85% with typical use. 97% is with perfect use

Pretty sure the percentage are based off of a years worth of use to the person with the average sex life, not every individual time having sex.

So like with perfect use there is only 3% chance of pregnancy over the course of an entire year, and like 15% chance with typical use over an entire year

Yep, the percentages are expressed per woman per year, which makes them pretty useless for consumers as far as actually quantifying the risk goes.

That's not how probability works. Probability only gives you the most likely scenario. However, even with a 99% chance to win you could lose 100 times in a row. It's utterly improbably, but entirely possible.

Also, that figure is in an ideal situation. It doesn't account for the woman's cycle, both parties' health, both parties fertility, sex positions, pre-use wear on the condom, etc. That being said, I think the main point in promoting condom use should be disease prevention.

Ogurisama posted...

That would mean after 98th time of having sex, you are prego

as you say, it's 3 out of 100, which is one out of ~33. so it'd be the 34th time, not the 98th. but really, it would just mean that you'd have a very high chance of it occurring by around the 34th time with roughly equal chance of happening earlier than that as later than that.
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Sahuagin posted...

Ogurisama posted...

That would mean after 98th time of having sex, you are prego

as you say, it's 3 out of 100, which is one out of ~33. so it'd be the 34th time, not the 98th. but really, it would just mean that you'd have a very high chance of it occurring by around the 34th time with roughly equal chance of happening earlier than that as later than that.

Also, the idea that 97% means that you will always get 3 out of 100 is called the 'gambler's fallacy'. The probability resets each time. You don't get more likely to 'win' after a string of losses.

Dash_Harber posted...

the idea that 97% means that you will always get 3 out of 100 is called the 'gambler's fallacy'. The probability resets each time. You don't get more likely to 'win' after a string of losses.

yeah, each event in isolation is strictly 97% (I'm just assuming that number is not made up of course which it probably is).

I'm not sure what I said is quite right but I don't know enough about it.

I want to say something like there's a tendency for it to be around the 34th event, spread like a bell curve around that point, with the first event as likely as the ~68th... but that can't be right.

it's possible the bell curve is spread between the first event and the 34th, so the tendency is for it to occur *on the way* to the 34th event. I have no idea though. almost want to try simulating it now and see what I get.
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Sahuagin posted...

Dash_Harber posted...

the idea that 97% means that you will always get 3 out of 100 is called the 'gambler's fallacy'. The probability resets each time. You don't get more likely to 'win' after a string of losses.

yeah, each event in isolation is strictly 97% (I'm just assuming that number is not made up of course which it probably is).

I'm not sure what I said is quite right but I don't know enough about it.

I want to say something like there's a tendency for it to be around the 34th event, spread like a bell curve around that point, with the first event as likely as the ~68th... but that can't be right.

it's possible the bell curve is spread between the first event and the 34th, so the tendency is for it to occur *on the way* to the 34th event. I have no idea though. almost want to try simulating it now and see what I get.

Yeah, I think you are right. I was just pointing out that it is still 'on average, it would take until your 34th try' and not 'your chances increase at the 34th try'. Also, I was directing it at the original post you quoted, and how he said that number 97 should guarantee pregnancy.

k after simulating it, I should have known better. the highest chance is for it to happen instantly, with steadily less chance after that. not sure the 34th event has any significance whatsoever, but I still sort of feel like it must.

graph of 100,000 attempts, saving how many tries it took to 'win' a 3% chance. (bottom scale is 1-100 tries with anything beyond that ignored). (not surprisingly there was about a 3,000/100,000 chance for it to occur on the first try.)



now I'm thinking, it must be the sum. not, "what is the chance that it happened AT this point", but "what is the chance that it happened UP TO THIS point".
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here's the accumulated chance, using the same data:



25% around 10 tries
50% around 25 tries
75% around 45 tries

so the 50/50 mark is around 75% of the way to the 'average', with it compressed on the left and stretched out on the right.
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Those percentages correspond to years according to the video so it's even less likely than we think.
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jramirez23 posted...

Those percentages correspond to years according to the video so it's even less likely than we think.

right, so then there'd be something like a 50% chance of failure over the course of 20-25 years.
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shadowsword87 posted...

That's not how that works, I hope you know.

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Sahuagin posted...

k after simulating it, I should have known better. the highest chance is for it to happen instantly, with steadily less chance after that. not sure the 34th event has any significance whatsoever, but I still sort of feel like it must.

graph of 100,000 attempts, saving how many tries it took to 'win' a 3% chance. (bottom scale is 1-100 tries with anything beyond that ignored). (not surprisingly there was about a 3,000/100,000 chance for it to occur on the first try.)



now I'm thinking, it must be the sum. not, "what is the chance that it happened AT this point", but "what is the chance that it happened UP TO THIS point".

Sahuagin posted...

here's the accumulated chance, using the same data:



25% around 10 tries
50% around 25 tries
75% around 45 tries

so the 50/50 mark is around 75% of the way to the 'average', with it compressed on the left and stretched out on the right.

Isn't charting it like that a perfect example of the gambler's fallacy? Doing it multiple times doesn't actually change the percentage of it happening each time.

Dash_Harber posted...

Isn't charting it like that a perfect example of the gambler's fallacy? Doing it multiple times doesn't actually change the percentage of it happening each time.

no, it's measuring something else. the first graph is "how many tries does it take to 'win'" with 100,000 data points.

ex: each roll of a (fair) die is always 1/6 but "how many rolls will it tend to take to get a 6" is a different question. chart for that looks like:



the second graph is almost the same data except accumulating which I then divided by 100,000 to get "what is the accumulated chance of it taking this many tries".

for a die, that looks like this:



notice that it very quickly soars towards 100% chance of having rolled a 6. if you roll a die 4 times you have a roughly 50/50 chance of getting a 6 or not. roll it 8 times and you have about a 75% chance of getting a 6. very likely with 20 or more rolls and almost 100% guaranteed with 30+ rolls.

note that there are probably better ways to calculate this kind of thing, but I'm a programmer not a mathematician/statistician. (though I'm learning to like statistics more and more and wouldn't mind learning a lot more about it.)

here it is calculated that the chance of rolling a 6 in 4 rolls is about 52% which matches my graph
https://math.stackexchange.com/questions/1000488/throw-a-dice-4-times-what-is-the-probability-6-be-up-at-least-one-time
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Sahuagin posted...

if you roll a die 4 times you have a roughly 50/50 chance of getting a 6 or not. roll it 8 times and you have about a 75% chance of getting a 6. very likely with 20 or more rolls and almost 100% guaranteed with 30+ rolls.

But that is the fallacy right there. Every single roll has a 1 in 6 chance, no matter how many times you have rolled previously.

Dash_Harber posted...

But that is the fallacy right there. Every single roll has a 1 in 6 chance, no matter how many times you have rolled previously.

That's true for any individual roll, not in aggregate. For example say you roll a die 98 times, on the 98th roll you have an exactly 1 in 6 chance, but he's talking about the probability of rolling a 6 given 98 rolls where each roll has a 1 in 6 chance.

Dash_Harber posted...

But that is the fallacy right there. Every single roll has a 1 in 6 chance, no matter how many times you have rolled previously.

the fallacy is to say that because there is a nigh-100% chance of rolling a 6 in about 30 rolls, that if you're on your 30th roll, then you are now almost guaranteed to get a 6.

it's kind of a matter of perspective, and where you are in time determining what you can accurately say about the future. if you haven't rolled your 30 rolls yet, then your chance of getting a 6 in 30 rolls is extremely high. but if you just rolled 29 times and didn't get one, then your chance of rolling one on the last roll (and thus all 30 rolls) has dropped to 1/6. and if you fail that last time, now it drops to 0% since they're all in the past.

actually now that I think of it, this is exactly why a rule of thumb that I go by is that doing something risky once is maybe dangerous, maybe not, but doing something risky over and over again (once a day or something) definitely IS dangerous and stupid. any risky thing you do regularly has one of these graphs, and is approaching 1 over time.
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*facepalm*

Our culture (that is, the U.S.) needs to be educated on the fact that non-penetrative sexual practices exist.
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is statistics really this fucking complicated? you have a 50/50 shot of getting pregnant every time you have sex, regardless of your birth control method. Either you get pregnant or you don't. people just like using OCPs because then they don't have to worry about losing feeling with a condom. it has nothing to do with how effective these methods are. Stop arguing about this nonsense "97% success rate" these are just numbers companies throw around to sound more enticing to buyers.


god I swear if I graduated high school I would be the next Einstein.
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Ogurisama posted...

shadowsword87 posted...

That's not how that works, I hope you know.

well percentage changed into a fraction would be 97/100, which as odds would be 97 out of 100 times

so 3 of the 100 times it doesnt work. Its all simple math

Except the times no pregnancy occurs don't stack. Every time it's a fresh 3% chance.
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It doesnt mean that out of 100 condoms 97 will work and 3 will fail

the failure rate is about 3% per year. This means that if 100 couples have regular sex for a year, using condoms correctly every time, 3 of the women will become pregnant. This is the same as the ‘97% effective’ statement that Ross read on the package.

http://www.embarrassingproblems.com/docspots/DocSpot-effectiveness-of-condoms

I_Abibde posted...

*facepalm*

Our culture (that is, the U.S.) needs to be educated on the fact that non-penetrative sexual practices exist.

Or, you know, just give them birth control and sexual education.