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Mathematics
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so we know that the average judge would have been 1 of 5 children, so the total number of brothers and sisters he had would add up to 4 , to make 5 including himself now since its equally likely to have a boy or a girl , that means on average half the children would be male and half would be female in total there would be 5/2 = 2.5 males and 5/2 = 2.5 females since all judges were men that means that the average judge would be male, and we have to take 1 from 2.5 to work out how many brothers he has: making it so he has 2.5 sisters and (2.5 - 1) = 1.5 brothers
oh wow...I didn't know I could just minus from the expected value when I have a confirmed observation (the judge himself in this case). thank you so much!! :)

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