1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Probability and children

  1. Dec 6, 2011 #1
    Question: What is the probability your 1st daughter is the 4th child?

    So probability of either male or female is .5 it seems probability of 3 boys in a row is .5*.5*.5 and then times again by .5 to get the answer (so .5^4). Is that correct? How would it change if you then switch that to the probability of 2nd daughter being the 4th child?
  2. jcsd
  3. Dec 7, 2011 #2


    User Avatar
    Science Advisor

    The probability that the 2nd daughter is the 4th child is the probability of getting two sons and one daugther, and then one daughter.

    If S stands for son, and D stands for daughter, the outcomes are


    all with the same probabilitiy (1/2)^4. Hence 3/2^4.
  4. Dec 7, 2011 #3


    User Avatar
    Science Advisor

    disregardthat, the question was "what is the probability that your fourth child is your first daughter?" You have answered "what is the probability that your fourth chile is your second daughter". Should we disregard that?

    In order that your fourth child be your first daughter, your first three children must be boys. Assuming that boys and girls are equally likely, the probability of that is [itex]1/2^3= 1/8[/itex]. Of course, then, the last child must be a girl and the probability of that is also 1/2. The probability the first four children are boys and the fourth a girl is (1/8)(1/2)= 1/16.
  5. Dec 7, 2011 #4


    User Avatar
    Science Advisor

    It was his second question.
  6. Dec 7, 2011 #5
    HallsofIvy gave you the answer to your first question (minus that typo, he meant first three children).

    Using his process, how do you think you can extend that to the second question? How, specifically, does the probability change.

    There is a line of thought that is helpful here, which I'll hint you to. There is only one way for the first 3 children you have to be boys, but that is not the case for the second question.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook