If you count people passing by you, and first 100 are all men, what is probability that 101th would be woman?

Question

Snoy:

If a father has 100 sons in a row,
then almost certainly there is something
with his DNA that makes female fetuses
almost unviable.

Answer 1

You are at a men's club. The probability that the next person is a man is at least 98%.

Answer 2

It is definitely not 50%. The odds of 100 men passing by you with 50% odds is 2^100 and that is too much of a long shot to dismiss as chance. There is no way to tell the exact odds without more details but I would estimate a 1% chance of seeing a woman.

Answer 3

If you say the answer is anything other than 1/2, it's because you are making up details as you go along.

Some answerers above say that if they see 100 men, then it's a strong indication that a lot of men are present. Another person would say that if they see 100 men pass by, there can't be too many left. Without details, the answer is 1/2.

RE: Lobster's answer.
I agree that if 100 men pass by in a row, the prob of that = 0.5^100. But if 50 men and 50 women pass by in an alternating fashion (M-W-M-W...), the prob of that is also 0.5^100.

Answer 4

With no other variables involved other than men and women equally being at this location... the answer would still be 50% chance(and this would also have to include that the 100 men that walked by were not excluded from the remaining group of people that could walk by)
... basically, we need more information to give you a real answer because there's probably another variable involved if the first 100 were men, and you have to discover that variable to make your study statistically significant(in a real world situation as opposed to a math test).

Answer 5

The probability is the same on matter how many men you counted, it could be ten thousand. There is a 50% the next person you walk by is a woman. (Unless your in some space completely dominated by men) But assuming that your in an open space with the population relatively half men half women the probability is 50%.

Just because the first 100 are men doesn't mean the 101st with be a man.

Likewise just because you've seen a hundred men walk by you doesn't mean that then 101st must be a woman.

Answer 6

This is similiar to a question I posed 7 months ago. See link. This is what I'd call a "meta-probability" question, because we're having to wonder about the odds of odds. If we note that the first 100 people passing by us are all men, the odds are that the odds of the next person being male isn't 1/2. An early thinker about this sort of problem is Thomas Bayes, after whom Bayesian theory is named.

Answer 7

Actually, the probability is indeed 50%. The question does not say "passing by you at a men's club". And similarly, if you have (however unlikely) 100 children, and they are all male, the probability that the 101st child is a female is STILL 50%.

There are two options, male or female. Always 50% in generic cases such as this one.

Answer 8

I think probably about 50 percent because 100 is small number compared to 6 billion people in the world. I'm not sure about the ratio of men to women though.

Answer 9

If we assume that the base probability of male/female for a single person is 0.5 then:

1) the probability of the 101st person being female "given" that the first 100 were male *is* 0.5

2) the probability of getting 100m|1f in sequence is 0.5^101, a very different number


You have to specify which probability more precisely to remove the ambiguity

Answer 10

Assuming that men and women are 50/50, then the odds would be 1-in-2. The odds do not change for each individual event regardless of what has happened before,