Children
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.
The chances of a mother giving birth to a son compared with a daughter are 55%-45% (This is true in the real world due to a higher male infant mortality rate although the percent might be closer together depending on the type of country. 1st world, 3rd world - more males are born than females)
In a family of four children, what are the odds a mother will have 2 boys and a girl?
Answer
I've listed all the possibilities b = boy g = girl
The chance of a child being male/female is independent, but the chance of having a certain order is just the probability multiplied by each other.
Because one child doesn't matter; the desired scenarios are any with either 3 boys 1 girl or 2 girls 2 boys.
I've marked with an X the desired outcomes, and at the end I have the probability of each occurrence.
Simply add the probabilities together for each desired case!
(as an eg of the calculation, bbgg is 0.55*0.55*0.45*0.45 which is the same answer as ggbb/ bgbg)
b bbb x 0.09150625
b bbg x 0.07486875
b bgb x 0.07486875
b bgg x 0.06125625
b gbb x 0.07486875
b gbg x 0.06125625
b ggb x 0.06125625
b ggg x 0.05011875
g bbb x 0.07486875
g bbg x 0.06125625
g bgb x 0.06125625
g bgg x 0.05011875
g gbb x 0.06125625
g gbg x 0.05011875
g ggb x 0.05011875
g ggg x 0.04100625
Answer is 0.6670125
or approx 2/3
(As a check all the probabilities should sum 1)
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Comments
klopper
Aug 15, 2002
| eh? |
Canary05
Aug 15, 2002
| I read this as a trick teaser - if there is 4 children then the possibility of them being 2 boys and a girl would be 0 (3 into 4 doesn't go). |
cathalmccabe
Aug 16, 2002
| The way I read it, it's in probability and makes perfect sense. If you could do the maths you would understand that there is whats called a don't care term - Just to make it a little more interesting! |
rufio
Aug 21, 2002
| yeah i agree.....2 boys and a girl is not 4 children |
MJs_Kitten
Aug 24, 2002
| thats 100000 too many numbers up there. who in hell would actually take the time to do that? Satan maybe. |
shop-a-holic
Aug 28, 2002
| I totally and 100% agree with Canary05 especially as I don't have da mathmatical ability 2 work it out anywayz! |
(user deleted)
Sep 01, 2002
| I am beginning to wonder if Cathalmcabe has actually got any of their teasers right? Neary every one I have seen is wrong or contains faulty information. |
StyLe89
Sep 04, 2002
| The guy meant 2 boys and 2 girls. Lighten up. |
doggyxp 
Sep 05, 2002
| I know so many of you have said it, but i'll say it again. in the teaser, it was stated that there was a family of FOUR. then it was stated, and i quote, "What are the odd of being 2 boys and one girl?" 2+1=3, the odds are zero because you can never have only three kids in a family of four kids. In this situation. |
StyLe89
Sep 07, 2002
| No, you're wrong. He said it was a family of four children but if you looked at the solution it clearly states that he meant 2 boys and 2 girls. He made a mistake. Big deal. |
dazza
Sep 13, 2002
| Why does the phrase "2 boys" have to mean "exactly 2 boys"? If I ask, "Do you have $10?" and you look in your wallet/purse and find $30, are you going to answer yes or no? I would say yes. Ergo: I think the answer to the problem is correct. |
Quax
Nov 07, 2002
| If you assume the puzzler means at least two boys and at least one girl, the calculation holds. |
snaps 
Nov 07, 2002
| I think some people need to go study some probability before commenting on these teasers. Four children, with two boys and one girl means that there are two possible scenarios that fit. Either there are two boys and two girls, or there are three boys and a girl. Both situations satisfy the criterion of there being two boys and a girl. The fourth child can be either a boy or a girl. |
jonnyonline
Jan 17, 2003
| snaps is right. the open ended "2 boys and 1 girl" is quite common with probability problems. it's implied that the fourth child can be either. by complaining that it doesn't explicitly state the two cases is to illustrate one's lack of experience with mathematics and statistics. |
tangerine
Feb 26, 2003
| AAAH. O.O Pardon me, but 0.0304384293583947593475934759375934759375 is a little much for me! @.@ You've ruined my brain :S
-Tangerine-  |
jimbo
Mar 14, 2003
| I disagree with the solution. You do not suspend common English in describing problems just because it is Mathematics. This is like a riddle "What has 2 legs and a long neck Answer: A giraffe, I didn't tell you about the other 2 legs." This might be fine as a joke but if you say there are 2 boys and a girl in the family you at least have to say at least!!! if you'll excuse the pun. 2 boys and a girl means 3 children. Those people who are arguing otherwise speak a different language to me. When you meet an old friend and ask if they have any children and they say 2 boys and a girl, then your normal reply would be "But how many children have you got?" or "What are the other ones then?" I don't think so! |
brainjuice
Apr 01, 2006
| "at least 2 boys and a girl" might be the best and avoid misunderstanding. (i actually dont speak english in my country so i dont wanna give many comments to the way you make a question)
your solution is too complicated. if there is a simple way why choose a complicated one? you can use "theorem on independent trials"
Theorem on independent trials:
let the probability of event E occuring be p. if this trial is repeated n times, the probability of E occuring exactly r times is:
nCr(p)^r(1-p)^(n-r)
the solution of your question will be:
p(2boy2girl)= 4C2(55%)^2(45%)^2= 0.3675375
p(3boy1girl)= 4C3(55%)^3(45%)= 0.299475
so the probability is: 0.3675375+0.299475= 0.6670125 (approx 0.67 = 2/3)
the answer is 2/3 |
ztodd
Oct 21, 2006
| Yeah, it's like saying I have a green eye and and a red hair.  |
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