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<blockquote data-quote="ichabod" data-source="post: 353665" data-attributes="member: 1257">No, that's the probability that if you take a picture of a random kid of his and it comes out male, that he has kids of two sexes. I saw nothing in the original question about the picture having been taken of a random child.Since people are throwing around probability formulas, let's go with the definition of conditional probability, namely P(E\F)=P(EF)/P(F). In english, that is the probability that E given F is true is equal to the probability of (E and F) divided by the probability of F.If the question is, given that we know he has at least one male child, what is the probability that he has children of different sexes, E = he has children of different sexes, and F = he has at least one male child.P(F) = 0.75 (Out of MM, MF, FM, and FF; 3 of the four give him at least one male child)P(EF) = 0.5 (Out of MM, MF, FM, and FF; 2 out of 4 give him at least one male child AND children of different sexes)Thus P(E\F) = 0.5 / 0.75 = 2/3 = 0.67I'm not sure why you are using Baye's theorem. You would use Bayes to find the probability of E by conditioning it on F and not F. You're getting the right answer for P(E), namely 0.5. However, the question was about P(E\F), not P(E).</blockquote>

[QUOTE="ichabod, post: 353665, member: 1257"] No, that's the probability that if you take a picture of a random kid of his and it comes out male, that he has kids of two sexes. I saw nothing in the original question about the picture having been taken of a random child. Since people are throwing around probability formulas, let's go with the definition of conditional probability, namely P(E\F)=P(EF)/P(F). In english, that is the probability that E given F is true is equal to the probability of (E and F) divided by the probability of F. If the question is, given that we know he has at least one male child, what is the probability that he has children of different sexes, E = he has children of different sexes, and F = he has at least one male child. P(F) = 0.75 (Out of MM, MF, FM, and FF; 3 of the four give him at least one male child) P(EF) = 0.5 (Out of MM, MF, FM, and FF; 2 out of 4 give him at least one male child AND children of different sexes) Thus P(E\F) = 0.5 / 0.75 = 2/3 = 0.67 I'm not sure why you are using Baye's theorem. You would use Bayes to find the probability of E by conditioning it on F and not F. You're getting the right answer for P(E), namely 0.5. However, the question was about P(E\F), not P(E). [/QUOTE]

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