If a couple has twins, and you know that at least one of them is a boy, what is the probability that they're both boys?

[Random Variable]

The answer is 1/3 (not 1/2) because you don't know which one is the boy. If you knew which one was the boy, then the probabilty would be 1/2.

 

[Anubis]

.999..... does in fact equal 1

 

[jst0ney]

its not illogical if you understand why

 

[Random Variable]

Originally posted by: Anubis
.999..... does in fact equal 1

I know it does. I took discrete math. But I still find it illogical.

 

[Random Variable]

Originally posted by: jst0ney
its not illogical if you understand why

I understand why.

There are four possibilites for the sex of twins in general: BB, GG, BG, and GB. Since in this case we know that it can't be GG, there are only three possibilities left. So the chances of two boys is 1/3.

 

[neutralizer]

Originally posted by: Random Variable

Originally posted by: jst0ney
its not illogical if you understand why

I understand why.

There are four possibilites for the sex of twins in general: BB, GG, BG, and GB. Since in this case we know that it can't be GG, then there are only three possibilities left. So the chances of two boys is 1/3.

And your point is? Thanks for showing us that you know stats. Kthxbye.

 

[daniel1113]

I prefer this probability "puzzle":

Imagine that the set of Monty Hall's game show Let's Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does.

The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn't hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors.

After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the car if she stays with her first choice? What if she decides to switch?

 

[illusion88]

Originally posted by: neutralizer

Originally posted by: Random Variable

Originally posted by: jst0ney
its not illogical if you understand why

I understand why.

There are four possibilites for the sex of twins in general: BB, GG, BG, and GB. Since in this case we know that it can't be GG, then there are only three possibilities left. So the chances of two boys is 1/3.

And your point is? Thanks for showing us that you know stats. Kthxbye.

Stats are importatn!

 

[Random Variable]

Originally posted by: neutralizer

Originally posted by: Random Variable

Originally posted by: jst0ney
its not illogical if you understand why

I understand why.

There are four possibilites for the sex of twins in general: BB, GG, BG, and GB. Since in this case we know that it can't be GG, then there are only three possibilities left. So the chances of two boys is 1/3.

And your point is? Thanks for showing us that you know stats. Kthxbye.

I thought that he thought that I didn't understand why, you smelly doody-head.

 

[aidanjm]

Originally posted by: Random Variable
The answer is 1/3 (not 1/2) because you don't know which one is the boy. If you knew which one was the boy, then the probabilty would be 1/2.

so they could be twins from the same egg, or "fraternal" twins from two different zygotes?

 

[myusername]

Actually you're wrong.

It's 5/9

One third of twins are identical.


edit: aidanjm was on the right track, but I was doing my research and math in the 3 minutes since he posted

 

[Random Variable]

Originally posted by: myusername
Actually you're wrong.

It's 5/9

One third of twins are identical.


edit: aidanjm was on the right track, but I was doing my research and math in the 3 minutes since he posted

What the heck are you talking about? This isn't a biology question. The question simply states that you know a couple who has twins, and you know that one of the twins is a boy.

 

[myusername]

Also, I came across an interesting idea while I was looking for the rate of identical twins.

it may be totally bunk, but check this out:

Charles E Boklage MD, and others have studied the vanishing twin, and it has been found to be more common than first realised. In one study, 325 twin pregnancies were identified very early by ultrasound exam and followed through the entire pregnancy. The study reported that 61 (18.8%) ended as twin births, 125 (38.5%) ended as singleton births, and 139 (42.8%) ended as a complete loss of the pregnancy. Generally, the vanishing twin f?tus is absorbed back into the uterus or degenerates as pregnancy advances. The likelihood of survival for the other co-twin is good.

Boklage has concluded that the "true" twinning rate is closer to 1 in 8 at conception. He feels that for every live-born twin pair, there are at least 6 singletons that have lost a twin without anyone ever knowing it. Some feel that the survival of just a few more of these twin conceptions could increase the twinning rate remarkably. This could be another explanation of why the rate of twins has recently increased.

Anyone may have had an undetected twin in the womb. It is conjectured that since twins are more likely to be left-handed than the normal population, left-handed singletons may be surviving co-twins of a vanishing identical.

whoa, goosebumps

 

[myusername]

Originally posted by: Random Variable

Originally posted by: myusername
Actually you're wrong.

It's 5/9

One third of twins are identical.


edit: aidanjm was on the right track, but I was doing my research and math in the 3 minutes since he posted

What the heck are you talking about? This isn't a biology question. The question simply states that you know a couple who has twins, and you know that one of the twins is a boy.

lmao

I think I got a D in statistical analysis, and even I know what I am saying ...

 

[mercanucaribe]

Originally posted by: Random Variable

Originally posted by: myusername
Actually you're wrong.

It's 5/9

One third of twins are identical.


edit: aidanjm was on the right track, but I was doing my research and math in the 3 minutes since he posted

What the heck are you talking about? This isn't a biology question. The question simply states that you know a couple who has twins, and you know that one of the twins is a boy.

It does matter whether they are fraternal or identical though, because there is a known ratio. If you said they were fraternal twins, it's another story.


Anyway, I don't think I believe that it's 1/3.

 

[Evadman]

Originally posted by: Random Variable
The answer is 1/3 (not 1/2) because you don't know which one is the boy. If you knew which one was the boy, then the probabilty would be 1/2.

Your english is mangled. If this were an actual word problem 1/3 would be wrong. You did not specify the order of the twins, and the ording of your question makes order meaningless. Therefore GB = BG th way you have it worded. Then there are only 3 possibilities, same sex or 1 of each. We know it is not GG, therefore, it must be either one boy one girl or both boys = 1/2.

We know in physics and probibilities the order, spin and other such things makes a huge difference. But if you are going to put out problems such as these, please be more specific. If that is EXACTLY the way your teacher put it, then your teacher needs to read the book again, or submit a publishing error to the publisher.

You know how schrodinger's cat can be dead or alive, and is actuly in both stats until someone opens the box and looks in? This works exacty the same way. By looking to see that one twin was a boy you colapsed the probability curve on that twin, but it still exists on the other. So until soeone looks at the second twin, you have exactly 2 options. A boy or girl. The twin is both till someone looks and the probibilties colapse and you end up with that twin being a girl or both boys. There is no other option.

 

[Random Variable]

Maybe I should change the question:

Behind two curtains there could be a donkey or a car (but nothing else). You know that a donkey is behind one of the curtains. What is the probabilty that donkeys are behind both curtains?

 

[mugs]

Originally posted by: daniel1113
I prefer this probability "puzzle":

Imagine that the set of Monty Hall's game show Let's Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does.

The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn't hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors.

After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the car if she stays with her first choice? What if she decides to switch?

1/3 if you stay, 2/3 if you change?

Or, your probability is 1 if you change to the right one or stick with the right one, and 0 if you change to the wrong one or stay with the wrong one.

 

[myusername]

Yeah, but that's a repost. I like this one, plus I get extra points

 

[myusername]

Originally posted by: mugs

Originally posted by: daniel1113
I prefer this probability "puzzle":

Imagine that the set of Monty Hall's game show Let's Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does.

The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn't hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors.

After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the car if she stays with her first choice? What if she decides to switch?

1/3 if you stay, 2/3 if you change?

Or, your probability is 1 if you change to the right one or stick with the right one, and 0 if you change to the wrong one or stay with the wrong one.

Isn't this philosophical, rather than statistical? Because even if you do not choose the "other" door you are CHOOSING the door from which you are not moving?

 

[Random Variable]

Originally posted by: Evadman

Originally posted by: Random Variable
The answer is 1/3 (not 1/2) because you don't know which one is the boy. If you knew which one was the boy, then the probabilty would be 1/2.

Your english is mangled. If this were an actual word problem 1/3 would be wrong. You did not specify the order of the twins, and the ording of your question makes order meaningless. Therefore GB = BG th way you have it worded. Then there are only 3 possibilities, same sex or 1 of each. We know it is not GG, therefore, it must be either one boy one girl or both boys = 1/2.

We know in physics and probibilities the order, spin and other such things makes a huge difference. But if you are going to put out problems such as these, please be more specific. If that is EXACTLY the way your teacher put it, then your teacher needs to read the book again, or submit a publishing error to the publisher.

You know how schrodinger's cat can be dead or alive, and is actuly in both stats until someone opens the box and looks in? This works exacty the same way. By looking to see that one twin was a boy you colapsed the probability curve on that twin, but it still exists on the other. So until soeone looks at the second twin, you have exactly 2 options. A boy or girl. The twin is both till someone looks and the probibilties colapse and you end up with that twin being a girl or both boys. There is no other option.

I did not specify the order because the order is not known. You just know that one of them is a boy. You don't know if the first one is the boy, or if the second one is the boy.


Here's a simple Maple program:

two_boys := proc ( n :: integer )

local count, k, firstkid, secondkid;

count := 0;
for k from 1 to n do

firstkid := 2; # 1 is a boy and 2 is a girl
secondkid := 2;

while firstkid = 2 and secondkid = 2 do # keep picking until both kids are not girls
firstkid := int_ran(1,2);
secondkid := int_ran(1,2);
end do;

if firstkid = secondkid then
count := count + 1;
end if;

end do;

return evalf(count/n);

end proc;


int_ran := proc( m :: integer, n :: integer )

round(evalf(m-0.5+(n-m+1)*rand()/999999999999))

end;


> two_boys(50000);

0.3336200000


EDIT:

Now if you know which one is the boy:

two_boys := proc ( n :: integer )

local count, k, firstkid, secondkid;


count := 0;
for k from 1 to n do

firstkid := 1;

secondkid := int_ran(1,2);

if firstkid = secondkid then
count := count + 1;
end if;

end do;

return evalf(count/n);

end proc;


int_ran := proc( m :: integer, n :: integer )

round(evalf(m-0.5+(n-m+1)*rand()/999999999999))

end;


> two_boys(50000);

0.5010200000

 

[BigJ]

You're question is worded horrendously.

If you say one of them is a boy, and then you say the other one, that indicates that you already know that one of them is a boy (which you were just talking about) and now you're talking about the other twin. Therefore, it is 1/2, not 1/3.

 

[BigJ]

Originally posted by: Random Variable
Maybe I should change the question:

Behind two curtains there could be a donkey or a car. You know that a donkey is behind one of the curtains. What is the probabilty that donkeys are behind both curtains?

The probability would be 0, because once again your question is worded horrendously.

"There could be either a donkey or a car behind each one of the two curtains."

 

[GhettoFob]

69%

 

[Random Variable]

Originally posted by: BigJ

Originally posted by: Random Variable
Maybe I should change the question:

Behind two curtains there could be a donkey or a car. You know that a donkey is behind one of the curtains. What is the probabilty that donkeys are behind both curtains?

The probability would be 0, because once again your question is worded horrendously.

"There could be either a donkey or a car behind each one of the two curtains."

All I said that you know a donkey is behind one of the two. I didn't say which one. And I left open the possibility that a donkey could be behind both. Did you have a rough day or something?