Tuesday, May 11, 2010
Problem 2: Three Children
On the first day of a new job, a colleague invites you around for a barbecue. As the two of you arrive at his home, a young boy throws open the door to welcome his father. “My other two kids will be home soon!” remarks your colleague.
Waiting in the kitchen while your colleague gets some drinks from the basement, you notice a letter from the principal of the local school tacked to the noticeboard. “Dear Parents,” it begins, “This is the time of year when I write to all parents, such as yourselves, who have a girl or girls in the school, asking you to volunteer your time to help the girls' soccer team.” “Hmmm,” you think to yourself, “clearly they have at least one of each!”
This, of course, leaves two possibilities: two boys and a girl, or two girls and a boy. Are these two possibilities equally likely, or is one more likely than the other?
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both options are equally likely. I know because the letter is addressed to anyone who has a girl, one or more, thus making the letter not personal to your family (as you might have one girl, or more than one).
ReplyDeleteI think that both options are equally likely. From the visit, I already know he has one son and one daughter. However, since the letter says "or girls" your colleague could have two girls. But, since it says "girl on the soccer team" he could have one girl and 2 boys. In conclusion, I think both are equally likely
ReplyDelete-Katty
It is equally likely for the colleague to have two boys and a girl or two girls and boy. I know the colleague has a son from when the son welcomed home his father. You also know that the colleague has at least one daughter from the note. This means there is one child left; it could be either gender.
ReplyDeleteMathematically my other post makes sense, but theoretically the third child is probably female. This is because there are more women then men in our world, thus their is a bigger chance that the child is a girl. The other post is probably the correct answer but this one also makes sense.
ReplyDeleteBased on the clues given in the question, it is equally likely that the third child is a boy or a girl. this is because you know the family has a boy, he was standing by the door, and you know that the familyhad a girl because there was a girls soccer tryout on the counter. There is a 50/50 chance that the 3rd child is either a boy or a girl, which means it is equally likely.
ReplyDeleteIt is equally likely that there are 2 boys and 1 girl or one girl and two boys. The reason for this is that the letter specifically says that "...who have a girl or girls in school." We already know that there is one boy and one girl, but there is no reason for the third child to be a boy or a girl, so you can assume whichever gender you want and there is a fifty-fifty chance that it will be a boy or a girl.
ReplyDeleteIt (as everyone else said) it is equally likely. There are 2 choices, so it's either one or the other, 50% or 50%. But, as Leo said, there are more girls than boys in the world, so it would be 52% chance the colleague has 2 girls, one boy and a 48% chance there are 2 boys and one girl.
ReplyDeleteIt would be more likely that there are two boys and a girl. I found statistics that show there are more women than men in the US but this does not mean that more girls are being born. It could be because men die earlier than women. I also found statistics that show more boys are born than girls in the US and the world. Assuming not many young children die in developed countries there should be more boys than girls. I have assumed the family lives in a developed country.
ReplyDeleteI think it is equally likely to have one girl and 2 boys or 2 boys and 1 girl. That is because the letter isn't adressed to a certain individual family, like that of the colleague (did i spell that right?:)It probably went to the whole student body so there really is no way to tell what the gender of the colleague's other kids are. Unless, Miss Dimitry, you are expecting us to reaserch the birthrate of boys to girls in the world or Canada or whatever and get into that whole deal of the scientific stuff. if so please tell me so I canreview my answer. but since it is a math blog I am sticking with all that up there ^ -emily
ReplyDeleteDavin I disagree with you
ReplyDeleteIf a parent has a boy or a girl their second baby is 33 percent more likely to be the same gender as the first baby(a nurse explained it to me while i was sitting in a waiting room). That means that it is more likely for there to be two boys and a girl
lol chris i don't think so! i don't think its going to be what u had first... i just think that 2 boys might just might be more likely because the man has XX and a woman has YX (i think thats what it is....) so it more common for it to be a boy, but in this scenario its equally likely....
ReplyDeleteit is an equal chance because there has to be 1 girl and 1 boy, the other can be one of the to options but it is not more likely for any gender baby to be born. also there are 2 possibilities, half of 4 is 2, half is 50%, that is an equal amount of chance. another way to describe it is there is a cake, half is chocolate, the other half is vanilla or well any flavour besides chocolate, this whole cake =100%, you blind fold your self and cut the cake, there is half chance youll get a chocolate, or vanilla. this half chance is 50%, that is half which shows each side has the same likelyness, inotherwords 100divided by 2=50=half=equal amount on each side(equal chance on each side)
ReplyDeleteAdele
Aaargh i hate it when my answer is the smae as the rest of them! Well i guess i will have to make do with it. I believe that it is equally likely because the letter addressed to parents with a girls who goes to the school, as it says "such as yourselves", and referring from the little boy who opens the door it means that there is indeed a boy and a girl in the household. as also the solleague says that he has 2 moe children coming. If thought that the colleague has only 3 children then it is equally likely for both o them to be chosen as only 2 of the genders have been chosen and the last child is unknown. If the colleague has more than 3 children because he only says that 2 are coming and there might possibly be more in the upstairs bedroom, or other places, then the question would be irrevelant.
ReplyDeleteLol chris, who said that the boy was older than the 2 children?
ReplyDeleteIt is more likely for there to be 2 boys and a girl than 2 girls and a boy. The chance of 2 boys and 1 girl is 2/3. The chance of 2 girls and 1 boy is 1/3. The way I found that out is that lets say we leave the 1 boy that we know is there already out. That would leave 2 children left. The way I put the pattern is form oldest to youngest. So lets say the were 2 girls, that is 1 possibility. Another possibility would be an older brother and a younger sister. The 3rd possibility is that there is an older sister and a older brother. There are 3 possibilities, they are
ReplyDelete.Girl Girl
.Older Brother, Younger Sister
.Older Sister, Younger Brother
2 of these possibilities leave 2 boys and 1 girl. 1 of the possibilities leave 1 boy and 2 girls. So since there are 3 possibilities and 2 are the 2 boys and 1 is the 2 girls, there is a 2/3 chance of 2 boys and 1 girl and a 1/3 chance of 2 girls and 1 boy.
I think it is equally likely that there are two boys and a girl, or two girls and a boy in your colleague's houshold. I figured that out because we know there has to be at least one boy and one girl. We know about the boy because he is at the front door, and we know about the girl because of the letter from the principal about girls' soccer teams. But you can't assume the third gender because you just know that it is a kid. It could be boy or girl, 50% a boy or 50% a girl. So therefore they are equally likely.
ReplyDeleteleo im luvin the name, leandro, nice, they equally likely the note said girl or girls so it is juzt wat is is, there is no chance havin one or the other so in the end its equal.
ReplyDeletethese two possibilities appear equally likely that they have one boy and two girls or two boys and one girl.
ReplyDeleteThat's my answer and I'm sticking to it!
i did hari i did
ReplyDeletenow SHUTUP!
also the oldest would be left home alone
ReplyDelete