Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    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!
    Offline

    1
    ReputationRep:
    :lolwut: Even I can do this.

    Tree diagram if you must?
    • Thread Starter
    Offline

    0
    ReputationRep:
    So how would you do it? Preferably without a tree diagram?
    • Thread Starter
    Offline

    0
    ReputationRep:
    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.
    • Thread Starter
    Offline

    0
    ReputationRep:
    Does no one know how to answer this question? Any help would be greatly appreciated!
    Offline

    15
    ReputationRep:
    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%.
    • Thread Starter
    Offline

    0
    ReputationRep:
    Thank you, I think it is just me looking for an overly complicated answer!
    • Thread Starter
    Offline

    0
    ReputationRep:
    THE ANSWER ABOVE IS WRONG, PLEASE COULD SOMEONE HELP.

    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!
    Offline

    18
    ReputationRep:
    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))
    • Thread Starter
    Offline

    0
    ReputationRep:
    (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?
    Offline

    4
    ReputationRep:
    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.
    Offline

    4
    ReputationRep:
    Sorry made a dumbass typo there.
    final result = B/[0.5(1-A+B)] so you're right
    Offline

    18
    ReputationRep:
    (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.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: January 29, 2010
The home of Results and Clearing

3,715

people online now

1,567,000

students helped last year

University open days

  1. SAE Institute
    Animation, Audio, Film, Games, Music, Business, Web Further education
    Thu, 16 Aug '18
  2. Bournemouth University
    Clearing Open Day Undergraduate
    Fri, 17 Aug '18
  3. University of Bolton
    Undergraduate Open Day Undergraduate
    Fri, 17 Aug '18
Poll
Will you be tempted to trade up and get out of your firm offer on results day?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.