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<blockquote data-quote="Xeriar" data-source="post: 352871" data-attributes="member: 4116">It's easier to break down the problem this way.You have three doors.&nbsp; Behind one lies the true prize.&nbsp; Behind the others, lies a goat (no prize).You pick a door.&nbsp; Doesn't matter which door, but you pick one.&nbsp; The host then reveals one of the doors, showing you the goat.You then get the opportunity to switch.If you're smart, you'll switch.&nbsp; Think about it - your chances of picking the right one initially was one third.&nbsp; That means, you have a two-thirds chance of sitting on a goat.&nbsp; The announcer revealing the other one being a goat -doesn't matter- because there will always be one to spare.---If you don't believe me, let's play a game.&nbsp;&nbsp; It costs $5 to play.&nbsp; Under one of three cups lies $10, under the others, a grain of rice.&nbsp; Once you pick a cup, I will reveal one of the grains of rice, and give you the opportunity to switch.Try it with yourself if you have to, seriously.The original question was plagued with a different problem, however.&nbsp; Knowing the gender of one child does not predict the other.&nbsp; You only know that he has a son, his other child is either a son or a daughter.</blockquote>

[QUOTE="Xeriar, post: 352871, member: 4116"] It's easier to break down the problem this way. You have three doors. Behind one lies the true prize. Behind the others, lies a goat (no prize). You pick a door. Doesn't matter which door, but you pick one. The host then reveals one of the doors, showing you the goat. You then get the opportunity to switch. If you're smart, you'll switch. Think about it - your chances of picking the right one initially was one third. That means, you have a two-thirds chance of sitting on a goat. The announcer revealing the other one being a goat [B]-doesn't matter-[/B] because there will always be one to spare. --- If you don't believe me, let's play a game. It costs $5 to play. Under one of three cups lies $10, under the others, a grain of rice. Once you pick a cup, I will reveal one of the grains of rice, and give you the opportunity to switch. Try it with yourself if you have to, seriously. The original question was plagued with a different problem, however. Knowing the gender of one child does not predict the other. You only know that he has a son, his other child is either a son or a daughter. [/QUOTE]

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