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Probability Question ....

M

macjock

macrumors regular
Original poster
May 30, 2008
200
0
Scenario 1. An expectant mother has been told she is giving birth to twins.

She wants to have a daughter, but does not mind what sex her other twin is.

Question 1. What is the probability that at least one of the twins is a girl?



Scenario 2. The doctor asks her whether she wants to find out the sex of her twins. She tells the doctor that she only wants to know whether she is having a girl, and the doctor confirms that she is. The doctor does not reveal the sex of the other child.

Question 2. Given that she knows one of the twins is a girl, what is the probability of the other one also being a girl?



NB: Assume that each baby has an equal chance of being either a boy or a girl.
 
Are you assuming that they are fraternal twins (two eggs) rather than identical twins (1 egg, split into two)?

If so, the answers are 3/4 and 1/3
 
To explain my answers from above. With two eggs, each of the two babys are equally likely to be male or female, so there are 4 equally likely scenarios:

MM MF FM FF

Since 3 of those 4 result in at least one female, the probability that at least one is a girl is 3/4

Now, for the second question. Since the doctor has told her that she is having a girl, there are only 3 possible scenarios:

MF FM FF

Each are equally likely, and only one of them results in 2 girls. So the answer is 1/3.
 
swiftaw said:
To explain my answers from above. With two eggs, each of the two babys are equally likely to be male or female, so there are 4 equally likely scenarios:

MM MF FM FF

Since 3 of those 4 result in at least one female, the probability that at least one is a girl is 3/4

Now, for the second question. Since the doctor has told her that she is having a girl, there are only 3 possible scenarios:

MF FM FF

Each are equally likely, and only one of them results in 2 girls. So the answer is 1/3.
Click to expand...

Wouldn't MF & FM be considered the same? So I would think the answer is 67% and 50%
 
macjock said:
I have the answer I just like the debate that these things can sometimes create.
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What sort of a debate can there be... there is only one correct answer. And to explain the answer from siftaw more... What swiftaw has done is created a sample space. The sample space contains all of the possibilities. However you can only create a sample space if all of those possibilities have an equal likelihood of occurring. So this sample space would be MF, FM, MM, FF. And in the question she said she wanted a girl. Because three of those have a female in them the answer is 3/4. And in the second question it says she knows one of them is a girl so we eliminate the MM possibility. Then the sample space is MF, FM, FF. So the answer is 1/3.

King Mook Mook

P.S. Do your own homework next time!
 
Research indicates that some men are more likely to have male children than and some more likely to have female. So in the real world approaching this as a simple probability question won't work.
 
Would it not be the 1/3th, 2/3rd, etc, as you don't have an equal chance of the spawn to be a boy as a girl? Like..isn't there a higher chance of there being a (boy/girl) than a (boy/girl)? (I don't know which one, so I put it in parenthesis)
 
fireshot91 said:
Would it not be the 1/3th, 2/3rd, etc, as you don't have an equal chance of the spawn to be a boy as a girl? Like..isn't there a higher chance of there being a (boy/girl) than a (boy/girl)? (I don't know which one, so I put it in parenthesis)
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Yes (I'm pretty sure it's better odds to have a girl), but if you had to do it with the actual probabilities it would be much more complicated and I'm guessing he is doing this for a 7th/8th grade (well this is when we do probability in Australia).

King Mook Mook
 
King Mook Mook said:
Oh aren't you a smarty pants! I bow before you!
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Smarter than you perhaps ?

I take it you failed your 8th grade?

FWIW I am long by the age where I will be getting homework, and as you can see even on here there are some slightly opposing views.
 
Question 1 answer is 3/4.

Question 2 is 1/2.
1/2 is the reason because I am assuming each event is independent of the other and since one is already a girl it means that it should have no effect on the out come of the other one which means it is 50/50
 
Rodimus Prime said:
Question 1 answer is 3/4.

Question 2 is 1/2.
1/2 is the reason because I am assuming each event is independent of the other and since one is already a girl it means that it should have no effect on the out come of the other one which means it is 50/50
Click to expand...

The answer to question 2 is not 1/2 it is 1/3.
 
Rodimus Prime said:
Question 1 answer is 3/4.

Question 2 is 1/2.
1/2 is the reason because I am assuming each event is independent of the other and since one is already a girl it means that it should have no effect on the out come of the other one which means it is 50/50
Click to expand...

swiftaw is correct. This is an example of the Monty Hall problem. The part that's tripping you up is that, while the conception of the twins is assumed independent and random, the reporting of them is not. The Doctor knows the sex of both, and preferentially selects the female to report. This skews the odds for the unreported one, which is thus more likely to be male.

If you change the question to say, "suppose the doctor selects one fetus at random and finds it to be female…" then the probability for the other is 50% just as your intuition suggests.
 
The biggest problem is the assumption that there's an equal chance of a male or female twin.

If it is known that the mother is pregnant with twins, it is actually far more likely that the twins are identical - meaning they would be the same sex.

But since the problem explicitly states otherwise, I concur with swiftaw and Gelfin, whose explanations are abundantly clear and correct IMO.
 
Tomorrow said:
The biggest problem is the assumption that there's an equal chance of a male or female twin.

If it is known that the mother is pregnant with twins, it is actually far more likely that the twins are identical - meaning they would be the same sex.

But since the problem explicitly states otherwise, I concur with swiftaw and Gelfin, whose explanations are abundantly clear and correct IMO.
Click to expand...

Which is why I prefaced my solution with the assumption that they are fraternal twins.
 
Until it is delivered, it is both a boy and a girl, reincarnated from the soul of Erwin Schrödinger.
 
Sydde said:
Until it is delivered, it is both a boy and a girl, reincarnated from the soul of Erwin Schrödinger.
Click to expand...

Only if you encase the womb in a lead box and introduce an IUD that automatically sorts sperm by sex chromosome, then uses particle decay to control a gate that allows only one type access. Then you get not so much quantum hermaphrodism as superposed chimerism.

Also lead poisoning.
 
Gelfin said:
Only if you encase the womb in a lead box and introduce an IUD that automatically sorts sperm by sex chromosome, then uses particle decay to control a gate that allows only one type access. Then you get not so much quantum hermaphrodism as superposed chimerism.

Also lead poisoning.
Click to expand...

I was going to try to follow up on Sydde's joke, but this beats anything I could have presented. The last part was a nice touch. :D
 
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