<p>HERE IT IS:</p>
<p>A woman and a man ( who are unrelated to each other) each have two children. At least one of the woman's children is a boy, and the man's older child is a boy. Which is more likely - that the man has two boys, or that the woman has two boys? Use probabilities to support you answer.</p>
<p>trick question: it’s jon and kate plus 8</p>
<p>hahahahahaha
extremely tough?</p>
<p>neither because you know at least one of them is a boy for each.</p>
<p>You can have four combos:</p>
<p>BB,BG,GG,GB (note: order matters)</p>
<p>The woman has a better chance. Man has 1/4th chance b/c his older child is a boy.</p>
<p>The woman. </p>
<p>The man’s oldest kid is a boy, but the women has atleast one boy.</p>
<p>Women: 50% Man:25%</p>
<p>I thought that question wasnt that hard? BTW I’ve never taken an AP Stats class or any type of stats class lol.</p>
<p>
It’s a shame that the latter half of your post destroyed any image of intelligence you attempted to convey in the former part.</p>
<p>Can someone explain this one…? I’m not in stat but I don’t understand y the women has a higher chance…</p>
<p>It’s a paradox from the 1960’s.</p>
<p>If your trying to share a paradox, specify it as so.</p>
<p>[Boy</a> or Girl paradox - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/Boy_or_Girl_paradox]Boy”>Boy or Girl paradox - Wikipedia)</p>
<p>"The Boy or Girl paradox surrounds a well-known set of questions in probability theory which are also known as The Two Child Problem[1], Mr. Smith’s Children[2] and the Mrs. Smith Problem. The initial formulation of the question dates back to at least 1959, when Martin Gardner published one of the earliest variants of the paradox in Scientific American. Titled The Two Children Problem, he phrased the paradox as follows:</p>
<pre><code>* Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls?
<p>Gardner initially gave the answers 1/2 and 1/3, respectively; but later acknowledged[1] that the second question was ambiguous. Its answer could be 1/2, depending on how you found out that one child was a boy. The ambiguity, depending on the exact wording and possible assumptions, was confirmed by Bar-Hillel and Falk,[3] and Nickerson.[4]</p>
<p>Other variants of this question, with varying degrees of ambiguity, have been recently popularized by Ask Marilyn in Parade Magazine[5], John Tierney of The New York Times[6], Leonard Mlodinow in Drunkard’s Walk.[7], as well as numerous online publications.[8][9][10] One scientific study[2] showed that when identical information was conveyed, but with different partially-ambiguous wordings that emphasized different points, that the percentage of MBA students who answered 1/2 changed from 85% to 39%."</p>
<p>the woman. men can’t physically have babies.</p>
<p>^thanks for the explanation. now I get it</p>
<p>Wait a sec. Using the logic from this Wikipedia article, it claims that if the older child has to be a male, then the possibilities are limited to BB or BG, making it a 50/50 chance. But in the case of the other parent, where there just has to be a boy and it doesn’t matter whether he’s older or younger, it claims that the possibilities are GB, BG, and BB. But if order matters that much can’t there be two ways to get BB? As in, B1,B2, or B2,B1. The original boy, assuming that he’s B1, can either be older or younger. If age/order matters for BG, why not BB? That would make it 50/50 for both parents. Sorry if my logic train is hard to follow, but can someone explain why this explaination is invalid? There are two possible ways to get BB.</p>
<p>Yeah, I have a wee bit too much free time.</p>
<p>no problem RAlec114. Just here to help.</p>
<p>I see what you’re saying supergenericman. I think you are right, and that’s why the question is ambiguous.</p>
<p>Consider four possibilities:</p>
<ol>
<li>The younger child is a boy, and the older child is a boy.</li>
<li>The younger child is a boy, and the older child is a girl.</li>
<li>The younger child is a girl, and the older child is a boy.</li>
<li>The younger child is a girl, and the older child is a girl.</li>
</ol>
<p>Now, it’s easy to see that these possibilities are exhaustive (assuming there are two children, of course), and even easier to see that they are mutually exclusive. And it’s not so obvious that you shouldn’t check to make sure, but each case has a probability of .25 .</p>
<p>The probability that the man has 2 boys is easy. Just divide .25 by .5 (eliminating the two cases in which his oldest child is not a boy), and you get that it’s 1/2.</p>
<p>Now, the other case is ambiguous, but not for the reason supergenericman stated; we already have probabilities for each of the mutually exclusive and exhaustive cases. The issue is, what do you mean by the probability you calculated?</p>
<p>Say that the probability is x. Now, one interpretation of that might be that if you take a random family of 4 with at least 1 male child, the probability of that family having 2 male children is x. That would give you the answer of 1/3.</p>
<p>But that’s not the only reasonable interpretation. Maybe you mean that if you take any random family of 4, the probability that the family has 2 male children, given that a randomly selected child is male, is x. Then the right answer is 1/2.</p>
<p>I say the odds are 50/50 for the man, and 25/75 for the woman.</p>
<p>We know that child #1 is male for the man. Child #2 is 50/50, so his odds are 50/50.</p>
<p>For the woman, the first child is 50/50 either way. If it’s a boy, the second is also 50/50, so 25% of the time yes, 25% of the time no.</p>
<p>If the first child is a girl, the second child MUST be a boy. So that’s another 50% no.</p>
<p>^ note that this isn’t quite accurate, because births are not actually quite 50/50.</p>
<p>Read the question literally. Explain how men can conceive.</p>