Probability question

Well, you have a 50% chance each time. But I have no idea what that adds up to.

Guessing 50%

Did I do this wrong? I drew out all of the possibilities, and 25.6% of them had two heads and two tails.
I never was very good at math...

As a result of not wanting to think, I decided to get out a coin and flip. Results: 2 heads, 2 tails.

Therefore, the correct answer to your question is 100%.

Dear All,

This question came up in a poker book... and it got me thinking?

there are 16 possible out comes when you flip a coin four times in a row. Let me show you":

H= number of heads flipped
T= number of tails flipped
n= # of possible outcomes in four coin flips


H=0... TTTT (n=1)
H=1... HTTT, THTT, TTHT, TTTH (n=4)
H=2... HHTT, HTHT,HTTH,THHT,THTH.TTHH (n=6)
H=3... HHHT, HHTH, HTHH,THHH (n=4)
H=4... HHHH (n=1)

Therefore,

n= 1+4+6+4+1

n=16

You see, of the 16 different possibilities, only 6 will result in two heads and two tails, hence ten out of 16 trials or 62.5% of the time there WONT be two heads,

HOWEVER................. most people would say 50%, and they would be the most accurate?.. Huh?

if you had said one head and three tails, you would be wrong 75% of the time, and if you said four heads or zero heads you would be wrong 93.75% of the time.

By choosing two heads, you chose the answer that minimized the probability of being incorrect,

That is the probability theory- minimizing errors

Ta dah

Whooooosh! Right over my head.

50%..you have an equal chance of both..
That..and 37.5 and 62.5 are sort of random..

uh

Wouldn't it highly depend on the coin itself?

37,5% : 16 possibilities, exactly 6 of them of the described type, and 6/16=0.375.

50% probability

Have no

My limited memory of probability tells me 50%. (That way if I'm wrong, I can just blame it on my poor memory, not on my lack of intelligence)

I am guessing 37.5%

50% just a quick guess.

I'm going to guess 37.5%

i beieve i recall from some old studies that the probabability on this was low, so I'm going with 37.5

I hang my head in shame

Lets see here. The standard deviation is about (n)^.5. Two coins have a 50% prob to have exactly 1. It HAS to be less than 50%. I know that it falls on a normal curve, and it actually equals the pascals triangle if you want THAT much trivia.

I've writtten a program a while back ago that simulates this. I've done up to 20 coin flips and did it several million times. I could go on.

Do the pascals triangle. It'll give you the answer.

Blaise Pascal....... The French father of Probability?

I think so.

I think 50% - is this a gambler question?

It was!

*sigh* idk im guessing

A man has two children. One of them is a boy. What is the probability that the other is a girl?

This is the a man cannot have children one, right?

No, no. It's a simple probability question. Perhaps I should have said, "A man fathers two children".

mmmmmm 50/50? one would suppose....... though there are things that influence this no?... The male decides the sex of his off spring, therefore... is it something like If he has a boy/girl he is more likely to have the same sex again.

I mean logically speaking it can only be either boy or girl 50/50 but I am wondering if there are any biological factors to take into consideration?

Similar to tossing a coin, heads or tails, right........ but, say for example you had sweaty hands, and you always flipped the coin starting with the "head" up on your thumb/finger.... would the weight of the moisture skew the reults? ............ and the answer is......?


Regards David

It's an example of a probability paradox. Like the Monty Hall problem and the one in this survey, the right answer and the natural intuitive answer is not necessarily the same thing.

The intuitive answer is 50% because girls and boys are equally likely at the point of conception. However, if you look at the wording, it doesn't specify which child (eldest or youngest) is the boy. It only states that one of them is boy.

Assuming girls and boys are equally likely, a two child family would consist of one of the following four configurations, all equally likely:

BB = 25%
BG = 25%
GB = 25%
GG = 25%

But since we know that one child is a boy, that discounts GG so we're left with 3 possibilities all equally likely

BB = 33%
BG = 33%
GB = 33%

Two of the three include a girl, so the answer is 2/3.

mmmmmmm I see, but isn't something flawed here?.......... follow me here, in my question I asked what are the chances of you flipping a coin four times in a row and having two heads and two tails .......... okay there are 16 possible outcomes with four flips in a row

Now, with your question and the way its phrased and your above breakdown, there can only be 3 possible outcomes

GG
BB
BG
(GB) does not count its the same answer as above......... as in my question

The fact that one is a girl or boy for that matter has no bearing on the what the other might be...... and which one is older or not has no bearing , as each time it could be boy or girl (forget any bilological considerations) quote A man has two children. One of them is a boy. What is the probability that the other is a girl?

So given this,.......
BB= 50%
BG=50%
GG= 0% as we already have a boy

Now in comparing it to my example, ask your self this:

If a man has flipped a coin twice, one of them was heads, what are the chances that the other will be a tail? ............ now tell me your answer, ?

HH....... 50%
HT........50%
TT.......... cant happen he's alreday flipped a head


But as a direct example to my question........... maybe

A man has four children, what are the odds he will have two boys and two girls?


Over to you,


Regards David

>Now, with your question and the way its phrased and your above breakdown, >there can only be 3 possible outcomes
>
>GG
>BB
>BG
>(GB) does not count its the same answer as above......... as in my question

BG and GB are two distinct outcomes. If they weren't, then in a given population the number of two child families with two boys would be roughly equal to the number of two child families of 1 boy and 1 girl (irrespective of which one was older than the other). This isn't true.

If 100 couples decided to have two kids then (assuming the split is always exactly 50/50) 50 couples would have a girl first and 50 couples would have a boy first. Of the 50 couples with a daughter, 25 would have another daughter and 25 would have a son. Of the 50 couples with a son, 25 would have another son and 25 would have a daughter.

So, if you would rather BG/GB were one group the population would be

GG = 25
BG = 50
BB = 25

That would change your set of probabilities from this:

>BB= 50%
>BG=50%
>GG= 0% as we already have a boy

to this

BB= 33.33%
BG=66.66%
GG= 0% as we already have a boy

Looking at your coin version of this question ( If a man has flipped a coin twice, one of them was heads, what are the chances that the other will be a tail?), then the answer is the same.

HH, HT, TH, TT are all equally likely to occur. Telling me that "one of them is heads" immediately discounts TT leaving 3 outcomes (still all equally likely). Two of them contain a Tail and one of them doesn't.

Like I said. Probability paradoxes are non-intuitive

mmmmm you may well be right certainly the logic sounds good.....ley me think on it more

Regards David

i just dont wanna guess