Probability question

[marcusnasland]

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What is the probability of having 2 girls followed by 2 boys followed by 2 girls followed by 2 boys... 8 children in total?

Im thinking 0.39%, but it is one of the end questions and they are usually harder so is there some sort of a trick to this?

 

[sciencegod]

I got 1.4%. streetwolf?

 

[Streetwolf]

What is the probability of having 2 girls followed by 2 boys followed by 2 girls followed by 2 boys... 8 children in total?

Im thinking 0.39%, but it is one of the end questions and they are usually harder so is there some sort of a trick to this?

Same as the probability of any 8 child combination, since it is a specific order.

You're correct. It is (1/2)^8 = 0.39%.

 

[sciencegod]

Same as the probability of any 8 child combination, since it is a specific order.

You're correct. It is (1/2)^8 = 0.39%.

with a deep sense of humbleness, the highest admiration and greatest level of respect and awe for mathgod, I would beg to differ.
please correct me if I'm wrong.

since youre not replacing kids, you can't just do (1/8)^8. you would do 1/8 * 1/7 * 1/6...
furthermore, that also would be incorrect. bec u the chance of picking the first boy is not 1/8. its 4/8 because there r 4 boys.

so I would do 4/8 * 3/7 * 4/6 * 3/5 * 2/4, etc. why is this wrong.

 

[CALgoob]

streetwolf is right. the probability of getting a girl as a second child is not 3/7, its just one half (why would it be less than 50%?). then the probability of getting every subsequent specific gendered child is one half.

it is a specific order so the math (as streetwolf said) is (1/2)^8

 

[sciencegod]

once u pick the first boy. there's only 7 left so isn't the chance of geting the next one 3/7

 

[sciencegod]

qccording to u guys if you would have just a boy and a girl. prob of getting boy first and girl second would be 1/2*1/2. that is clearly wrong. I would de 1/2 * 1/1. and that's correct. what's the diff in this case.

 

[CALgoob]

boy first and girl second IS 1/4 (draw out the tree if you have to). having two children with one girl and one boy in any order would be 1/2.

the original question was asking for a specific order.

 

[Streetwolf]

with a deep sense of humbleness, the highest admiration and greatest level of respect and awe for mathgod, I would beg to differ.
please correct me if I'm wrong.

since youre not replacing kids, you can't just do (1/8)^8. you would do 1/8 * 1/7 * 1/6...
furthermore, that also would be incorrect. bec u the chance of picking the first boy is not 1/8. its 4/8 because there r 4 boys.

so I would do 4/8 * 3/7 * 4/6 * 3/5 * 2/4, etc. why is this wrong.

No what you're doing is starting with a family of 8 kids (4B / 4G) and one-by-one choosing them to do whatever.

If I said there's a family of 4B 4G and you need to sit them down in a row of 8 chairs, what is the probability of seating them in the order GG-BB-GG-BB then you'd be correct.

The probability of having a girl first is 1/2. The probability of having a girl second is 1/2. The probability of having a boy third is 1/2. You can look at all 8 births separately. Together you just multiply all those 1/2s and get (1/2)^8.

Not (1/8)^8 which is what you said in your reply to me.

 

[sciencegod]

No what you're doing is starting with a family of 8 kids (4B / 4G) and one-by-one choosing them to do whatever.

If I said there's a family of 4B 4G and you need to sit them down in a row of 8 chairs, what is the probability of seating them in the order GG-BB-GG-BB then you'd be correct.

The probability of having a girl first is 1/2. The probability of having a girl second is 1/2. The probability of having a boy third is 1/2. You can look at all 8 births separately. Together you just multiply all those 1/2s and get (1/2)^8.

Not (1/8)^8 which is what you said in your reply to me.

sorry man. yea I misundestood the q. I thought it meant you have 8 kids and you want to line them up 2 boys then 2 girls, etc.

my mistake. now that I read the q again it means to give birth to 2 boys then 2 girls.

but just to make sure, the way I did would have been right if the question was to line them up that way, right?

calgoob , that's what I meant when I said to line up a boy and girl, it would only be 2 ways.

I j

 

[marcusnasland]

Thanks alot guys!