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On the morning of January 1, a hospital nursery has 3 boys and some number of girls. That night, a woman gives birth to a child, and that child is placed in the nursery.
On January 2, a statistician conducts a survey and selects a child at random from the nursery. The child happens to be a boy. What is the probability the child born on January 1 was a boy? Thanks for this.

 May 30, 2017
 #1
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0.50

 May 31, 2017
 #2
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According to our teacher, the answer is 4/7, not 1/2 but have no idea how he gets that.

 May 31, 2017
 #3
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Assume there are g number of girls. So we have a total of: g+3 children. The newly-born child has a 50% chance of being a boy, in which case will have: g+4 children. It also has a 50% chance of being a girl, in which case will have: g+1+3=g+4 children.


Then the probability of selecting a boy and the newly-born child is a boy is: 4/[g+4]*1/2.
The probability of selecting a boy and the newly-born child is a girl is: 3/[g+4]*1/2.
Then the probability of selecting a boy =4/[g+4]*1/2 + 3/[g+4]*1/2 =3.5/[g+4].

 

Finally, the probability of being born a boy, given the probability of selecting a boy(calculated above) is: {4/[g+4]*1/2} / {3.5/[g+4]} =2/3.5 =4/7.

 May 31, 2017

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