I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?
No.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.
Yes.Do I need to know this?
No. To clarify, here are the rules:Is the answer slightly under 1/3 because of the probability of a hermaphrodite child?
Congratulations.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.
Well, you don't need to know it was Tuesday. The probability would be the same for any named day of the week.Do I need to know this?
Here's how I'd look at it:I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?
I've spotted the flaw in this. The family with 1 boy born on Tuesday will always say "Tuesday". But the family with 2 boys only one of which is born on a Tuesday will not always say"Tuesday". So these options listed with asterisks are not equally likely.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.
I was thinking about this again and I realised that there is another flaw in the expected solution. The difficulty is to know what one can infer from this statement. There's no problem with the statement about having two children implying that its a typical family with the usual equal probabilities of:I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?