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# Maths Probability Question watch

1. What is the probability of having all girls from 4 successful births(a set of twins counts as one birth)? Take the chance of having a boy and a girl to be equal (1 in 2) and the chance of having twins is 1 in 72. Bear in mind you can have boy boy twins, girl girl twins, boy girl twins and girl boy twins. Does the order of births matter?

Discount any birth of more than two, so no triplets, and don't include miscarriages or still births or anything like that.

Can you work this out?
2. P(have all single girls from single births) = ((71/72)*0.5)^4 = ...
P(have 3 single girls and 1 set twin girls) = ((71/72)*0.5)^3*((1/72)*0.5*0.5)) = ...
P(have 2 single girls and 2 sets of twin girls) = ((71/72)*0.5)^2*((1/72)*0.5*0.5))^2
P(1,3) = ....
P(0,4) = ...

P(all girls from 4 births) = P(4,0) + P(3,1) + P(2,2) + P(1,3) + P(0,4)
3. I don't think P(all single girls) = 0.5*0.5*0.5*0.5 because there is only a 71/72 chance that each girl is a single

By your method the P(all girls from 4 births) > 1/16 which shouldn't be true because adding in the small chance of adding twins should mean the P drops slightly below 1/16

I think Doivid's answer just needs a factor of 71/72 next to the single girls then it's correct
4. (Original post by Aihara)
I don't think P(all single girls) = 0.5*0.5*0.5*0.5 because there is only a 71/72 chance that each girl is a single

By your method the P(all girls from 4 births) > 1/16 which shouldn't be true because adding in the small chance of adding twins should mean the P drops slightly below 1/16

I think?
I was going to consider that in my answer, however I don't think the question is looking for this because the probabilities that the OP described add up to 1 and 1/72. Obviously this shouldn't be the case, but I think the whoever wrote the question didn't want to bother lowering the chance of having a single boy or single girl to accommodate twins.
5. ok yeah, I see the wording of the question does seem to imply that
6. (Original post by Aihara)
ok yeah, I see the wording of the question does seem to imply that
forget what I said before, I agree with you now

I misread the question as saying take the chance of having a single boy or girl as equal, when it doesn't include the word single

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Updated: February 13, 2010
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