riddle...tanya and bill each have two children...?

G

gabs

New member
tanya and bill each have two children. we know that at least on of tanya's children is a boy and that bill's oldest child is a boy. explain why the probability that tanya has two boys does not equal the probability that bill has two boys.
 
We don't know which of Tanya's children is the son.
Let me demonstrate with a diagram let b stand for boy and g stand for girl and the first letter will stand for the first child and the second for the second child.

normally the possibilities would look like:
bb
bg
gg
gb

however for Tanya we only know she does not have two girls so her possibilities are:
bb
bg
gb

for Bill we know the first child is a boy so his possibilities are:
bb
bg

the probability of Tanya have two boys is 1/3 and Bill is 1/2
 
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