Page 2 of 2 FirstFirst 12
Results 16 to 19 of 19

Thread: Family of Three Children - Conditional Probability

  1. #16
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    6,580
    Thanks
    2913

    Re: Family of Three Children - Conditional Probability

    Quote Originally Posted by joshuaa View Post
    Yeah the problem (b) cares about boys, especially the older brother and (B) B B event has boys. Why do we have to exclude it?
    we don't exclude it

    there are 6 ways the boys can be ordered. thus each way has probability 1/42

    in 4 of those orders the "boy" has an older brother.

    Thus BBB contributes 2/21 to the overall probability.

    There are 3 other combos with 2 boys contributing 1/14 each for a total probability of 13/42
    Follow Math Help Forum on Facebook and Google+

  2. #17
    MHF Contributor

    Joined
    Aug 2006
    Posts
    22,405
    Thanks
    3296
    Awards
    1

    Re: Family of Three Children - Conditional Probability

    Quote Originally Posted by romsek View Post
    This is all exactly as I would have (and did) do it. You care about the boys because the problem asked for the
    probability of an older brother. Not an older sister.
    (c) is correct. Any combination of 2 B's and 1 G satisfies this. There are 3 of them.
    Quote Originally Posted by joshuaa View Post
    Yeah the problem (b) cares about boys, especially the older brother and (B) B B event has boys. Why do we have to exclude it?
    These two quotes prompt me to ask if either of you have had any training in formal logic?
    The two logical connectives, and & or serve similar functions while being totally at odds.
    $P\text{ and }Q$ means that both P & Q must be true; while $P\text{ or }Q$ means that at least one of them is true.
    So if a boy has an older brother and a younger sister then that is only one case $\bf{BBG}$ There can be no other.
    So if the question were: In a family of three children, what is the probability that a boy has an older brother and a younger sister? Then the answer is $\dfrac{1}{8}$.

    Now if the question were: In a family of three children it is known that at least one is a boy, what is the probability that boy has an older brother and a younger sister?
    Follow Math Help Forum on Facebook and Google+

  3. #18
    Super Member
    Joined
    Mar 2012
    Posts
    523
    Thanks
    14

    Re: Family of Three Children - Conditional Probability

    if (B) is the older brother

    why are (B) B B, (B) B G, (B) G B, and G (B) B not considered as the boy has an older brother?
    Follow Math Help Forum on Facebook and Google+

  4. #19
    Super Member
    Joined
    Mar 2012
    Posts
    523
    Thanks
    14

    Re: Family of Three Children - Conditional Probability

    Quote Originally Posted by Plato View Post
    These two quotes prompt me to ask if either of you have had any training in formal logic?
    The two logical connectives, and & or serve similar functions while being totally at odds.
    $P\text{ and }Q$ means that both P & Q must be true; while $P\text{ or }Q$ means that at least one of them is true.
    So if a boy has an older brother and a younger sister then that is only one case $\bf{BBG}$ There can be no other.
    So if the question were: In a family of three children, what is the probability that a boy has an older brother and a younger sister? Then the answer is $\dfrac{1}{8}$.

    Now if the question were: In a family of three children it is known that at least one is a boy, what is the probability that boy has an older brother and a younger sister?
    Plato

    here i will do this
    at least one boy means
    probability of one boy + probability of two boys + probability of three boys
    or just 1 - probability of zero boy

    which is 1 - 1/8 = 7/8

    so probability is (1/8) / (7/8) = 1/7

    but BBG has equiprobability
    if (B) is the older brother, then
    probability of (B)BG = B(B)G = 1/14

    then the answer will be 1/14 because only B(B)G satisfies the condition
    Follow Math Help Forum on Facebook and Google+

Page 2 of 2 FirstFirst 12

Similar Math Help Forum Discussions

  1. Replies: 18
    Last Post: Mar 11th 2014, 02:10 PM
  2. 3 children, probability of boy/girl = 0.5 EASY!
    Posted in the Statistics Forum
    Replies: 1
    Last Post: Sep 18th 2012, 12:06 PM
  3. Replies: 7
    Last Post: May 17th 2011, 06:51 AM
  4. Conditional probability - family with blue eyes
    Posted in the Statistics Forum
    Replies: 3
    Last Post: Oct 9th 2010, 04:46 PM
  5. Replies: 4
    Last Post: Jun 9th 2009, 08:56 AM

Search Tags


/mathhelpforum @mathhelpforum