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Firls, firls, firls

Posted by Chris on January 17, 2011 – 12:07 pm

I ‘m from planet X. On planet X our children are firls and moys. The probability that our firstborn child will be a firl is 3/4 After the firstborn, the probability of the next born being the same type as the previous child is 3/5.

I have three children. They are not all moys. What is the probability that all three are firls?

There is no intentional misdirection in the question this time

This post is under “Logic” and has 18 respond so far.

18 Responds so far- Add one»

1. 1. Karl Sharman Said：

9/20? But with my track record……

2. 2. Chris Said：

Hi Karl. That’s right. Your track record hasn’t improved
The probability is lower than that.

I was just about to re-edit it to make the answer be 1/4 (or 1/3). But I won’t bother now.

3. 3. cazayoux Said：

27/91?

4. 4. DP Said：

27/100 female girls (redundant), I mean ‘firls’, is the answer without “rescale”. The 9/100 moys should then be subtracted as stated in the problem, so…27/91

the 27/100 is 3/4 * 3/5 * 3/5 = (3*3*3)/(4*5*5) = 27/100
the 9/100 is 1/4 (from 1 – 3/4) * 3/5 * 3/5 = (1*3*3)/(4*5*5) = 9/100

5. 5. Bekki Said：

P(3 firls | not all moys) = P(3 firls)/P(not all moys) = (3/4 * 3/5 * 3/5) / (1- (1/4*3/5*3/5)) = 27/91

6. 6. Chris Said：

Three right answers. What’s the probability of that?

Well done folks.

7. 7. Bekki Said：

Well, the experimental probability seems to suggest that it’s 3/4.

8. 8. Karl Sharman Said：

My first thought was 27/100, but then I thought that the probability of the 3rd child sex was redundant as it would be the same as the 2nd child, so didn’t need to be calculated in. Don’t ask why, but I got it into my head that if the second child was a firl then the 3rd would be a firl – 100% probability.
Naturally I would still have been wrong as I didn’t remove the 9/100 moys.
On the bright side I can see where I went wrong. But enough about that, let’s go back to Girls Girls Girls… one more time – how does it go….?

9. 9. Chris Said：

Hi Bekki. I assume you’re trying a PC proggy. I think it must have a bug.

Hi Karl. You’re improving.

I’ve done than is required, but only because of possible extra questions.

```MMM  1/4 * 3/5 * 3/5 =  9/100
MMF  1/4 * 3/5 * 2/5 =  6/100
MFM  1/4 * 2/5 * 2/5 =  4/100
MFF  1/4 * 2/5 * 3/5 =  6/100
FMM  3/4 * 2/5 * 3/5 = 18/100
FMF  3/4 * 2/5 * 2/5 = 12/100
FFM  3/4 * 3/5 * 2/5 = 18/100
FFF  3/4 * 3/5 * 3/5 = 27/100
```

For any who think otherwise, that table shows that e.g. MMF, MFM and FMM are not “the same thing”.

10. 10. Bekki Said：

My experimental probability was that 4 people answered and 3 were correct. Is that what you were referring to?

11. 11. Chris Said：

12. 12. Chris Said：

Minor pedantry.
P(FFF | !MMM) = P(FFF & !MMM) / P(!MMM)
But as FFF & !MMM = FFF that’s OK.

13. 13. Bekki Said：

I know the formula (#12) but I was just too lazy to write it all out. lol.

14. 14. Chris Said：

Hi Bekki. I actually had assumed that you knew. I just wanted to make sure that everyone was aware of it.

15. 15. angela Said：

hi this is rlly complicated i dont understand it..you guys are too smart for me, LOL

16. 16. shalini Said：

i guess its 1/3

17. 17. duane1969 Said：

3/4 + 3/5 + 3/5 = 9/14

There is a 9 in 14 chance that they are all firls.

18. 18. Chris Said：

Hi duane1969, that would be true if you didn’t know that they weren’t all boys.

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