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<blockquote data-quote="The Sigil" data-source="post: 351899" data-attributes="member: 2013">Simple:For each of the man and the woman there are four possibilities, with equal probability of each occurring (assuming that there is truly a 50% probability that a given child is born Male or Female).For the woman:1.) MM2.) MF (older is male, younger is female)3.) FM (older is female, younger is male)4.) FFThat's simple - there are two combinations of &quot;one of each&quot; and two combinations of &quot;both the same sex&quot; so the odds are 50-50 that she has &quot;one of each.&quot;So the answer to A is &quot;50%&quot;.For the man:1.) MM2.) MF (older is male, younger is female)3.) FM (older is female, younger is male)4.) FFThe fact that he shows a picture of him with a son eliminates possibility four, leaving us with...1.) MM2.) MF3.) FMAll of these have equal probability, so there is a 67% chance that the man has children of both sexes.&nbsp; It does NOT change the probability to &quot;we know child 1 is male, whether he is older or younger, hence child 2 has a 50-50 chance of being male or female and hence there is a 50% chance of him having one of each&quot; (a common mistake).&nbsp; We're assuming the picture gives us more information than it does... if he had said, &quot;this is my oldest child and is my son&quot; it would have eliminated possibility 3, thus lending a 50-50 chance.THAT'S why the answer to B is 67%.--The Sigil</blockquote>

[QUOTE="The Sigil, post: 351899, member: 2013"] Simple: For each of the man and the woman there are four possibilities, with equal probability of each occurring (assuming that there is truly a 50% probability that a given child is born Male or Female). For the woman: 1.) MM 2.) MF (older is male, younger is female) 3.) FM (older is female, younger is male) 4.) FF That's simple - there are two combinations of "one of each" and two combinations of "both the same sex" so the odds are 50-50 that she has "one of each." So the answer to A is "50%". For the man: 1.) MM 2.) MF (older is male, younger is female) 3.) FM (older is female, younger is male) 4.) FF The fact that he shows a picture of him with a son eliminates possibility four, leaving us with... 1.) MM 2.) MF 3.) FM All of these have equal probability, so there is a 67% chance that the man has children of both sexes. It does NOT change the probability to "we know child 1 is male, whether he is older or younger, hence child 2 has a 50-50 chance of being male or female and hence there is a 50% chance of him having one of each" (a common mistake). We're assuming the picture gives us more information than it does... if he had said, "this is my oldest child and is my son" it would have eliminated possibility 3, thus lending a 50-50 chance. THAT'S why the answer to B is 67%. --The Sigil [/QUOTE]

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