- #1
- 22,183
- 3,321
I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?
Start with an apparently simpler problem:Matterwave said:50%
Nathanael said:Is it perhaps 6/14? (I'm only guessing this based on the fact that the 1/2 is wrong, but I still feel it should be 1/2 :tongue:)
I won't explain myself unless I am confirmed correct (for the sake of not giving out too many hints).
micromass said:.. born on a Tuesday..
micromass said:None of the numbers in this thread are answers to the original question yet.
Psinter said:In order to be another boy it NEEDS to be born on another Tuesday. There are 7 days a week and you can only have another every 9 months. Once the ninth month is hit there are only 21 days available for the child to be born. Not more, not less. In those 21 there are only 3 Tuesdays, which means:
3/21 = 1/7 = 14.something%
But all the other days are girls, which means there's somewhat 85% chance it will be a girl. Therefore, you had roughly 14% chances of having another boy.
drizzle said:Do I need to know this?
Matterwave said:Is the answer slightly under 1/3 because of the probability of a hermaphrodite child?
Matterwave said:Well, I guess we can list out all possibilities. The first column being the gender and the second column being the day:
BMBM BMBT BMBW BMBTH BMBF BMBS BMBSU
BTBM BTBT BTBW BTBTH BTBF BTBS BTBSU ...
BMGM BMGT BMGW BMGTH BMGF BMGS BMBSU...
GMBM GMBT GMBW GMBTH GMBF GMBS GMBSU...
GMGM GMGT GMGW GMGTH GMGF GMGS GMGSU...
Each block has 49 entries. The GG block is eliminated.
In the first block there are 13 entries with at least 1 boy born on Tuesday. In the second block there are 7 entries with a boy born on Tuesday, and in the third block there are 7 entries with a boy born on Tuesday. That's 27 total entries with a boy born at least on Tuesday. Of those 27 entries 13 are both boys while the other 14 have girls in them. So the probability is 13/27.
drizzle said:Do I need to know this?
drizzle said:Do I need to know this?
micromass said:I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?
Vanadium 50 said:PeroK starts in the right place.
There are three possibilities per child, which I will label as G, for a girl, T for a boy born on Tuesday, and N for a boy not born on a Tuesday. Ordering the children, here are the outcomes and their probabilities:
GG = 1/4 = 49/196
GN = 3/14 = 42/196
NG = 3/14 = 42/196
GT = 1/28 = 7/196 *
TG = 1/28 = 7/196 *
NN = 9/49 = 36/196
NT = 3/98 = 6/196 *
TN = 3/98 = 6/196 *
TT = 1/196 = 1/196 *
We are told one child is a boy born on Tuesday. That means we are in one of the 5 asterisked outcomes.Of them, the outcomes with two boys are NT, TN and TT, for a probability of 13/27.
micromass said:I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?
Yeah. Therefore, 50% :)Borek said:Perhaps my English fails me, but the answer to the question whether "one is a boy born on a Tuesday" means "if the other is a boy, he wasn't born on a Tuesday" is not obvious.
mfb said:The frequentist approach does not work here as the children are either boys or girls (each) - there is no actual probability involved. It is possible to take the Bayesian approach - but then we also have to ask "given the different girl/boy combinations, how likely is it to get the information 'at least one is a boy born on Tuesday'?". And there is no meaningful way to assign a specific probability to that.
E: Less than 1% (see below), because we confuse English meaning with Math meaning.bluntwcrackrap said:Better one:
What is the probability of getting this question right?
A:25%
B:50%
C:60%
D:75%
The probability of having two boys is 1/4 or 25%. This is because there are four possible outcomes when having two children: BB, BG, GB, and GG. Only one of these outcomes results in having two boys (BB).
No, the gender of the first child does not affect the probability of having two boys. Each child has an equal chance of being either a boy or a girl, regardless of the gender of the other child.
Yes, the probability of having two boys changes with each pregnancy. Each pregnancy is an independent event, meaning the outcome of one pregnancy does not affect the outcome of another. Therefore, the probability of having two boys remains at 1/4 for each pregnancy.
The probability of having two boys if the first child is already a boy is 1/2 or 50%. This is because there are only two possible outcomes for the second child (B or G) and only one of those outcomes (B) results in having two boys.
No, the probability of having two boys is not the same for all families. While the overall probability is 1/4, the actual outcome can vary for each family. Some families may have two boys, some may have two girls, and some may have one of each. It all depends on chance and the independent events of each pregnancy.