Steven G
Elite Member
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- Dec 30, 2014
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Assume that a child has an equal chance of being born on any month and of either gender (male, female). Let p be the probability that given that a family has two children and at least one of them is a girl, both are girls. Furthermore, let q be the probability that given that a family has two children and at least one of them is a girl born in April, that both are girls. Does p=q? The answer is no but I do not see why yet.
Here is what I have done so far.
The 1st scenario. The family has two children and at least one is a girl. So the family has either gb, bg or gg. In one of the three cases there is a 2nd girl. So p=1/3. I am certain that this is correct.
2nd case. The family has two children and at least one is a girl born in April.
The family can have either bg(girl in April), gb(girl in April), gg (1st girl in April) or gg (2nd girl in April). Note that the 'other girl' (if there is one) could have been born in April as well.
Now in the 1st case the given girl could have been born in any of the 12 month and in this case we are told April.
So is the answer for q, q= 2/4 = 1/2 because we have 4 cases in the 2nd scenario? Well that is only true if the four possibilities are all equally likely. I am not totally convinced that that is true.
Any takers on how to explain this? Thanks
Here is what I have done so far.
The 1st scenario. The family has two children and at least one is a girl. So the family has either gb, bg or gg. In one of the three cases there is a 2nd girl. So p=1/3. I am certain that this is correct.
2nd case. The family has two children and at least one is a girl born in April.
The family can have either bg(girl in April), gb(girl in April), gg (1st girl in April) or gg (2nd girl in April). Note that the 'other girl' (if there is one) could have been born in April as well.
Now in the 1st case the given girl could have been born in any of the 12 month and in this case we are told April.
So is the answer for q, q= 2/4 = 1/2 because we have 4 cases in the 2nd scenario? Well that is only true if the four possibilities are all equally likely. I am not totally convinced that that is true.
Any takers on how to explain this? Thanks