to ask how you work out odds of something

[Northend77]

Not really an AIBU but posting here for traffic

How do you work out the odds of multiple things? For example - a baby has a particular feature (that a few others have but is not genetic) and was born/conceived via a certain method (which makes the feature less likely)?

I can probably find the statistics for each thing on their own but my maths is failing me to work out how to combine the odds!!

You mean what is the odds of having a blue eyed, blond haired baby who also has a birthmark in the shape of a frog?
Blue eyed = 25% chance
Blond hair = 20% chance
Frog birthmark = 10% chance
Chance of getting all of these in 1 child = 25% 20% 10% = 0.5%

You have a penny it's either heads or tails..
so you have a one out of two chance of tails.

You add in that your throwing a dice which has 1 in 6 chance of a 6
So a tails and a number 6 is
2 X 6 so 1 out of 12...

You add in a certain penny out of 100 other penny's
2 x 6 x 100.. 1 out of 1200......

so to get a tails, a 6 and the penny you want is 1 chance in 1200.

the easiest way it to do an odds tree essentially.

So you put the "first" chance first (if they are independent it doesn't matter which is first), with branches for each option (e.g. Red or black, heads or tails, has x disease or doesn't), with the odds of each on the branch and then at the end of each branch the option. Then at the end of each of the options do another tree for each of the second thing.

Then multiply through to give the total chance of each thing (eg red and a king).

www.onlinemathlearning.com/probability-tree-diagrams.html

Thank you both, that's exactly what I needed!! Now to do some research!

Cath is correct in his/her maths, but it sounds like there are just too many variables.

Plus it is kind of a nonsense to talk about the 'odds' of a baby having or not having a feature - just say it's a ten percentage chance that the baby has the aforementioned frog-shaped birthmark, and you really would rather it didn't. Your baby is born with the birth mark - what are you going to do? Send it back? Feel aggrieved?

I'm intrigued by the feature that is NOT genetic?

@Cath2907 your maths is off there. The odds of having all those things is 0.005%.

OP, if you know that 3 out of 5 people do X activity, then they odd are 3/5. This is equal to 6/10 or 60% or a 0.6 chance.

The odds of having multiple things is worked out by multiplying the odds.

Be careful you have your wording correct though. The odds of having a girl in one single pregnancy is 0.5. The odds of one woman having two girls is 0.25 (0.5x0.5). However this doesn't not alter the fact that the second pregnancy itself has a 0.5 chance of being a girl.

Cath's example only works if eye colour and hair colour are statistically independent (broadly speaking, there is no correlation). But if blond hair is more common amongst those with blue eyes (which I suspect it will be), then you can't multiply the percentages like that.

@Cath2907 your maths is off there. The odds of having all those things is 0.005%.
Nope Cath 2907 is correct. ClaudiaWankleman I thnk you are confusing 0.25 x 0.2 x 0.1 = 0.005 with 25% x 20% x 10% = 0.5%

ok, I was deliberately trying to be vague because the actual statistics come across as very goady and I was hoping to avoid that because I'm not, I'm just genuinely interested to know the odds.

SendintheArdwolves It's not a feature, as in a birth mark, but that was the only example I could think of! It's a particular APGAR score against method of birth and number of babies. It's a really trivial thing but I just wanted to be able to say to my little girl that she's 1 in xxxxxx million (and have the actual odds). Silly really. I'm now not even sure if APGAR scores are recorded anywhere other than on paper as I can't find actual statistics

But thank you for your maths help. If I can get the stats then I know how to work it out now

Can someone explain to me why I'm wrong?

Also you'd need to be sure that all the occurrences are truly independent and not related through some underlying factor.

Silly example : chances of a baby being a boy is 50% (say), and chances of a baby having an un-descended testicle is 8% (say). Chances of your baby being a girl and having an undescended testicle is not 4%, it's 0%.

Typically most conditions are related in various (known and unknown) ways so probabilities can't be multiplied as neatly as that. You might better off looking at the rarest condition you're interested in, and then looking at co-morbidity of your secondary condition of interest with the first.

Claudia
25% x 20% x 10% = 0.005 - that's true
But 0.005 is 0.5% (to see this, remember 0.01 is 1/100 or 1% so 0.005 is half of that).

So
25% x 20% x 10% = 0.5% - also true

@ClaudiaWankleman and @Cath2907 You are at cross purposes.

A probability of 0.005 (measured on a scale of 0=impossible and 1=certain) is the same as a % chance of 0.5% (measured on a scale of 0=impossible to 100%=certain)

so 25% x 20% x 10% =0.5% - it has to be - 25% (a quarter) of 10% is 2.5%, and 20% (a fifth) of 2.5% is 0.5%.

In probability terms - 0.25 x 0.2 x 0.1 = 0.005

They are the same.

Thanks. I had missed the fact that the two numbers were in effect identical.

So OP you can get independent stats for each of those. eg : chance of triplets is X%, chance of c-sec is Y%. But you can't multiply those to say chance of triplets needing c-sec id X times Y %.

Not sure I'm explaining myself correctly, but you'd need a different stat of what is the probability of triplets needing a c-sec. That's likely to be much much higher than just a normal singleton birth needing a c-sec.

And likely to be confounded by other factors - such as normal singletons not typically getting c-secs unless there is medical necessity whereas triplets may get c-secs without any debate just for safety.

So a singleton needing a c-sec much more likely to be an emergency situation with lower APGAR score, and one of triplets delivered by c-sec.

If the features are statistically independent, multiply the chances of each by each other.

eg, If I was to roll a dice and flip a coin at the same time, and I wanted to get both a heads and a 6 then the chances of that happening would be:

1/2 X 1/6
Or
50% X 16.667% = 8.333%

But if the different things are statistically related it is harder to work out. Eg, if you were trying to work out the probability that a child was both male and colour blind, you could not just multiply the overall chance of a baby being born male by the overall incidence of colour blindness within the population, because boys are more likely than girls to be born colour blind anyway. You would have to multiply the probability of a baby being born male by the probability of males being colour blind to get the correct answer.
I hope that makes sense.

Thanks everyone. I have also spoken to a couple of midwife friends who don't know if I'll find the statistics without trawling through midwifery journals so I'll just settle for a rough made up estimate!

I just wanted to be able to say to my little girl that she's 1 in xxxxxx million (and have the actual odds). Silly really

Well, yes, it is a bit silly - you can tell your little girl she's one in eight billion.

It's great to foster a feeling in your kids that they are special, unique, loved, etc, but I'm not sure that the "medical miracle" way is the best way to do this. That's one of those weirdly passive things - the child didn't do anything to be "special" in that way, and encouraging them to be proud of thing that is an accident of birth kind of smacks of magical thinking.