Let n=4 and i-1=2. Why ans is 0.687500?
We have 6 variants:
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0011
=> Waiting time = 0+0+2+1=3
   Conditional expectation(0011) = 0*(1/4)+0*(1/4)+2*(1/4)+1*(1/4)=3/4
   Probality(0011)=(1/4)*(2/4)+(1/4)*(1/4)=3/16

0101
=> Waiting time = 0+1+0+1=2
   Conditional expectation(0101) = 0*(1/4)+1*(1/4)+0*(1/4)+1*(1/4)=2/4
   Probality(0101)=(1/4)*(1/4)+(1/4)*(1/4)=2/16

0110
=> Waiting time = 0+2+1+0=3
   Conditional expectation(0110) = 0*(1/4)+2*(1/4)+1*(1/4)+0*(1/4)=3/4
   Probality(0110)=(1/4)*(1/4)+(1/4)*(2/4)=3/16

1001
=> Waiting time = 1+0+0+2=3
   Conditional expectation(1001) = 1*(1/4)+0*(1/4)+0*(1/4)+2*(1/4)=3/4
   Probality(1001)=(1/4)*(1/4)+(1/4)*(2/4)=3/16

1010
=> Waiting time = 1+0+1+0=2
   Conditional expectation(1010) = 1*(1/4)+0*(1/4)+1*(1/4)+0*(1/4)=2/4
   Probality(1010)=(1/4)*(1/4)+(1/4)*(1/4)=2/16

1100
=> Waiting time = 2+1+0+0=3
   Conditional expectation(1100) = 2*(1/4)+1*(1/4)+0*(1/4)+0*(1/4)=3/4
   Probality(1100)=(1/4)*(2/4)+(1/4)*(1/4)=3/16

ans = Expected value = Sum(Conditional expectation(mask) * Probality(mask))
ans = (3/4)*(3/16)+(2/4)*(2/16)+(3/4)*(3/16)+(3/4)*(3/16)+(2/4)*(2/16)+(3/4)*(3/16)=(3/4)*(3/16)*4+(2/4)*(2/16)*2=3*(3/16)+2*(2/16)=11/16.


Edited by author 21.06.2017 12:40