Wabbit Posted January 12, 2011 Share Posted January 12, 2011 I'm curious how many people here can figure these out (don't use the internet! honor system.) 1. I have two kids. One is a boy. What is the probability I have two boys? 2. I have two kids. One is a boy born on a Wednesday. What is the probability I have two boys? Quote Link to comment Share on other sites More sharing options...
Cr(+)sshair Posted January 12, 2011 Share Posted January 12, 2011 No probability because there's only one boy! Quote Link to comment Share on other sites More sharing options...
LazaHorse Posted January 12, 2011 Share Posted January 12, 2011 Both would be 25% chance. The first condition of having a boy/girl doesn't really matter as the chance of having two of either starts at 25% (1/2 chance compounded once). Propagation of errors in these two 1/2 chances might yield a slightly different answer, but I'm pretty sure its 25%. Unless I'm missing something, the being born on a Wednesday thing shouldn't alter the answer unless you are going by statistical data of what happens when a child is born on a Wednesday. That data would theoretically pan out to having no correlation anyway. Thanks for this, as a Physics major, I need something at least slightly educational during my winter break lol... Quote Link to comment Share on other sites More sharing options...
Wabbit Posted January 12, 2011 Author Share Posted January 12, 2011 No probability because there's only one boy! One is a boy = you know one is a boy, the second is unknown, i just need the % of probability that the second is a girl or boy. Quote Link to comment Share on other sites More sharing options...
Wabbit Posted January 12, 2011 Author Share Posted January 12, 2011 Both would be 25% chance. The first condition of having a boy/girl doesn't really matter as the chance of having two of either starts at 25% (1/2 chance compounded once). Propagation of errors in these two 1/2 chances might yield a slightly different answer, but I'm pretty sure its 25%. Unless I'm missing something, the being born on a Wednesday thing shouldn't alter the answer unless you are going by statistical data of what happens when a child is born on a Wednesday. That data would theoretically pan out to having no correlation anyway. Thanks for this, as a Physics major, I need something at least slightly educational during my winter break lol... Girl Girl Girl Boy Boy Girl Boy Boy since I've told you that one of the children is a boy, you can ignore Girl Girl of the three remaining possibilities, only one (Boy Boy) has the second child as a boy, so the answer is 1/3 the first question is not a difficult one to answer, the actual challenge is in the second one, and it's completely counterintuitive. i'll write up the solution at some point soon. As for the second question (of course assuming that the births are independent events and that there is an equal probability of a boy and a girl, and an equal probability of being born on each of the seven days of the week): First, we need to map out the complete set of events: but not yet =p Quote Link to comment Share on other sites More sharing options...
n1ckkkkk Posted January 12, 2011 Share Posted January 12, 2011 50%. Quote Link to comment Share on other sites More sharing options...
Wabbit Posted January 12, 2011 Author Share Posted January 12, 2011 50%. the reason this isn't just a straight up conditional probability question, is because I did not tell you which child is the confirmed boy. if I had, then obviously the choices for the other child are 50/50. an easy way to conceptualize it is: imagine we have a (random) group of 1 million families with 2 kids each. if we asked every family with at least one boy to step forward, you'd guess that about 750,000 of them would. then of those families, if we asked those with two boys to step forward, about 250,000 or so of them would. Quote Link to comment Share on other sites More sharing options...
Jella Posted January 12, 2011 Share Posted January 12, 2011 And this is why I didn't go to stats class. Quote Link to comment Share on other sites More sharing options...
n1ckkkkk Posted January 12, 2011 Share Posted January 12, 2011 cool Quote Link to comment Share on other sites More sharing options...
Wabbit Posted January 12, 2011 Author Share Posted January 12, 2011 And this is why I didn't go to stats class. [video=youtube;mhlc7peGlGg] Monty Hall Paradox Enjoy and do it lol Ignore youtube comments plz =] Quote Link to comment Share on other sites More sharing options...
Mike is Fr3sh Posted January 12, 2011 Share Posted January 12, 2011 [video=youtube;mhlc7peGlGg] I'll use this knowledge the next time I'm on a gameshow. Quote Link to comment Share on other sites More sharing options...
Rudabaga Posted January 12, 2011 Share Posted January 12, 2011 Left Quote Link to comment Share on other sites More sharing options...
Wabbit Posted January 12, 2011 Author Share Posted January 12, 2011 I'll use this knowledge the next time I'm on a gameshow. lol^ Quote Link to comment Share on other sites More sharing options...
Arclyte Posted January 12, 2011 Share Posted January 12, 2011 And this is why I didn't go to stats class. This Quote Link to comment Share on other sites More sharing options...
Wabbit Posted January 13, 2011 Author Share Posted January 13, 2011 As for the second question (of course assuming that the births are independent events and that there is an equal probability of a boy and a girl, and an equal probability of being born on each of the seven days of the week): First, map out the complete set of events: Child A / Child B: Boy on Wednesday / Girl (any of the days) - 7 outcomes Girl (any of the days) / Boy on Wednesday - 7 outcomes Boy (any of the days) / Boy on Wednesday - 7 outcomes Boy on Wednesday / Boy (any of the days) - 6 outcomes (remember: you have counted one of these outcomes in the above scenario) Of these outcomes, 13 fit the proposed scenario - a boy born on Wednesday and another boy. Therefore, the correct answer is 13/27 If you need help visualizing this, you can make (or imagine) a 14 x 14 grid of all possible combinations (first child - girl monday, second child - girl monday; first child - girl monday, second child - girl tuesday, etc.) If you then restrict the set to any case that includes a boy born on a Wednesday, you should get 27 cases. Of these, the cases that include another boy should total 13 cases. Quote Link to comment Share on other sites More sharing options...
Dr.jiggles Posted January 13, 2011 Share Posted January 13, 2011 At least one of you children is a boy and born on Wednesday do i win. Quote Link to comment Share on other sites More sharing options...
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