Punnet square genetics proportion question

Punnet square question?

True breeding punnet square?

I got the right answer but need some clearing up.

true-breeding dwarf and true breeding maize plants produced all dwarf plants in F1 . in the f2 generation dwarf and tall plants segregated 3:1 ratio. Dwarf F2 plants self pollinated. what proportion of the resulting plants would be expected dwarf

let BB=Dwarf bb=tall

BBXbb

F1= 1 Bb

Bb x Bb

F2=1 BB:2 Bb: 1bb

now it gets tricky..

so there is a 1/3 chance that BB x BB

but a 2/3 chance that Bb x Bb...what I am confused about is what about the chance Bb x BB?

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if BB and BB were crosses all offspring would be BB(dwarf)

4/4=1 *1/3= 1/3

if Bb and Bb were crossed 3/4 would be dwarf so

3/4* 2/3=6/12+1/3= 10/12= 5/6 proportion expected to be dwarf?

Edited May 19, 201114 yr by samiam99