Thread: best forecast

hi,
i have been solving this question and my result is different than the results i have been given to compare to. can u please tell me if i am correct?
two people flip coins X,Y count their heads respectively.
T=max(x,y) Z=min(x,y)
if it is given that t=2. what is the best forecast for z.

i created a table of mutual probability of t and z.
now i think i should find
e(z|t=2)
i got e(z|t=2)=0+1*0.25*16/7+2/16*16/7=6/7

am i correct or is the answer 20/23

thanks for your help

I need to know how many times, these people are tossing their coins.