Uniform Distribution - probabilities

mathstats

New Member
Hi guys, I am trying to solve an exercise but it seems to bem somehow strange.
It is an experiment where A believes that men are bigger than women but B doesn't believe that, since A wants to convince B thatn ran an experiment and called randomly a number and ask to the person who answered the phone to say his height and his wife's height (if he is married). So we have two number (m,w) and the difference d=m-w.
So I have the difference groups: G1: 0 to 10cm, G2: 10 to 20cm...G10: 90 to 100cm and G0: less than 0cm.
Assume that in the city of A and B the height distribution of married people is equally distributed between 1m and 2m, both for men and women.
I wanna calculate the propabilities of each group above. I have the sample space X={G0, G1,...G10}
and now I want to calculate p(G0), p(G1), ..., p(G10).

Since they are uniform distributed the density should be f(x)=1/b-a = 1/(2-1) = 1
P(G1)=P(0<=x<=0.1(10 cm))=0.1/1=0.1 which is not true, because the book gives these probabilities and I just don't know how to do it, it says:

P(G0)=1/2
P(G1)=9.5/100
P(G2)=8.5/100
...
P(G10)=0.5/100

What am I missing?