statistical problem about twin-criminals

The following data comes from an investigation of one-egged twins'
kriminalitet.
OMM = means one-egged twins where the two twins are male.
OFF = means one-egged twins where the two twins are female.
200 OMM did not commit a crime
81 OMM committed a crime where only one of the twins did it.
50 OMM committed a crime where both twins did it.

306 OFFdid not commit a crime
18 OFF committed a crime where only one of the twins did it.
4 OFF committed a crime where both twins did it.

Investigate if the material can be described by the following statistical
model and interpret it:

P(both are not criminal)=p^2
P(only one (exactly) is criminal) = 2p(1-p)
P(both are criminals)=(1-p)^2


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