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"They're twins, and I wanted him to have a cool name! How could I have known she was not a boy!"


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Wierd resolution on this screenshot

But the jest is that after several kids, William the Conquerer decides to try the other side of the fens at the age of 52
 
Nope, one in sixteen. Getting five sons in a row would be "flipping tails five times in a row" too, so 2 in 32 i.e., 1 in 16.

Why 2 out of 32? It's definitely 1 / (2^5) = 1/32. Let's do it the "stupid way" by writing out all possibilities:

Code:
1  FFFFF
2  FFFFS
3  FFFSF
4  FFFSS
5  FFSFF
6  FFSFS
7  FFSSF
8  FFSSS
9  FSFFF
10 FSFFS
11 FSFSF
12 FSFSS
13 FSSFF
14 FSSFS
15 FSSSF
16 FSSSS
17 SFFFF
18 SFFFS
19 SFFSF
20 SFFSS
21 SFSFF
22 SFSFS
23 SFSSF
24 SFSSS
25 SSFFF
26 SSFFS
27 SSFSF
28 SSFSS
29 SSSFF
30 SSSFS
31 SSSSF
32 SSSSS
 
Why 2 out of 32? It's definitely 1 / (2^5) = 1/32. Let's do it the "stupid way" by writing out all possibilities:

Um, yes, that's exactly what I mean. There's thirty-two permutations. Permutation one has five daughters. Permutation two has five sons. Two permutations out of thirty-two have the kids all the same. 2/32 = 1/16.
 
But no ones talking about having all kids the same, just having 5 daughters. So 1/32
 
But no ones talking about having all kids the same, just having 5 daughters. So 1/32

No-one's talking about having five daughters -- the OP question was "what are the odds of flipping tails five times in a row", which I answered. If it were "What are the odds of the first five flips of a coin being tails", it's 1 in 32, which is what the others are mistakenly answering. If it's just "five times in a row", you get the first one for free, so to speak, since the run starts with a tail by definition and has a 100% chance, not 50% like people often assume.
 
No-one's talking about having five daughters -- the OP question was "what are the odds of flipping tails five times in a row", which I answered. If it were "What are the odds of the first five flips of a coin being tails", it's 1 in 32, which is what the others are mistakenly answering. If it's just "five times in a row", you get the first one for free, so to speak, since the run starts with a tail by definition and has a 100% chance, not 50% like people often assume.

Yeah, good point. You gotta flip a daughter first for the chance of a second probability of the same.
If you flipped a boy first then it would be the same (doh) but is the question different if we say "same gender" starting with 0 children?