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# Probability and Statistics watch

1. Hello everyone, please could someone give me some help on how to answer this question as I am confused, thank you!

Suppose that the probability that two twins are both boys is 'A', and that both are girls is 'B'. Also, suppose that when the twins are of different sexes, the probability that the first born is a girl is 1/2. If the first born twin is a girl, what is the probability that the second is also a girl?

THANK YOU!
2. Even I can do this.

Tree diagram if you must?
3. So how would you do it? Preferably without a tree diagram?
4. Well logical I get

Sample Space is (GB, BB, BG, GG) and if the first is a girl then we have the event space of (GB, GG) left so surely this implies that we get a 1/2. But how does this fit in with the question in hand? I am confused.
5. Does no one know how to answer this question? Any help would be greatly appreciated!
6. Probabilities of independant events don't change in relation to past events. If you have two kids and the first is a boy, then the probability that your second kid is a boy is still 50%. The chances of getting two boys in a row is 50% * 50% = 25%, but you already know that one is a boy so the probability that the other is a boy is 50%.
7. Thank you, I think it is just me looking for an overly complicated answer!

Hello everyone, please could someone give me some help on how to answer this question as I am confused, thank you!

Suppose that the probability that two twins are both boys is 'A', and that both are girls is 'B'. Also, suppose that when the twins are of different sexes, the probability that the first born is a girl is 1/2. If the first born twin is a girl, what is the probability that the second is also a girl?

THANK YOU!
9. I am quite bad with probability.

We want

P(girl | first born is a girl)
which is equal to

= P(girl and first born is a girl)/P(first born is a girl)
= P(girl girl twin)/P(first born is a girl)

using the conditional probaility thing (also using the fact the question says given that we have twins)

P(first born is a girl) = P(first girl | mixed twins) + P( first girl | same sex twins)
= 1/2 + P(girl | same sex twins)

Further, P(girl | same sex twins)= P(girl girl twin)/P(same sex twins) = B/(A+B)

so we get P(girl | first born is a girl)= B/(1/2 + B/(A+B))
10. (Original post by silent ninja)
I am quite bad with probability.

We want

P(girl | first born is a girl)
which is equal to

= P(girl and first born is a girl)/P(first born is a girl)
= P(girl girl twin)/P(first born is a girl)

using the conditional probaility thing (also using the fact the question says given that we have twins)

P(first born is a girl) = P(first girl | mixed twins) + P( first girl | same sex twins)
= 1/2 + P(girl | same sex twins)

Further, P(girl | same sex twins)= P(girl girl twin)/P(same sex twins) = B/(A+B)

so we get P(girl | first born is a girl)= B/(1/2 + B/(A+B))
Thank you for your help, though I thought that

P(first born is a girl) = P(first girl | mixed twins)P(mixed twins) + P( first girl | same sex twins)P(same sex twins)

and this would imply the answer would be

B / (B + 0.5(1-A-B)

would this be correct?
11. Well sample space = MM,FF,MF,FM w/ P(MM)=A, P(FF)=B => P(FM) + P(MF) = 1-A-B

Here we'll use the theorem of total probability that says P(A|B)P(B)+P(A|B')P(B') = P(A) when B and B' form a partition of the sample space, to find P(1st's child is a girl) which out of laziness i'll say is P(F*)
P(F* | FM or MF )P(FM or MF)
P(FM or MF) = P(FM) + P(MF) =1-A-B because they're disjoint events.
P(F* | FM or MF ) is given and is 1/2
hence P(F* | FM or MF )P(FM or MF) = 0.5(1-A-B)

P(F* | not (FM or MF) )P(not (FM or MF) ) which by cond prob is [ P(F* AND ( FF or MM))/P(FF or MM)][P(FF or MM)] = P(F* AND (FF or MM))= P(FF) =B

So adding them together we get P(F*) = 0.5(1-A+B)

Now we want P(FF | F*) which is easy = P(FF AND F*)/P(F*) = P(FF)/P(F*) =B/[0.5(1-A+B)] ta da.
12. Sorry made a dumbass typo there.
final result = B/[0.5(1-A+B)] so you're right
13. (Original post by zcomputer5)
Thank you for your help, though I thought that

P(first born is a girl) = P(first girl | mixed twins)P(mixed twins) + P( first girl | same sex twins)P(same sex twins
oops, that looks right, using that rule which I have demonstrated I can't use.

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