Given the exact same question and answer here: https://crypto.stackexchange.com/a/37212/40935.
How does one derive/figure out (using equation, combination of equations, or "knowledge") the bold marked parts in the following:
How does one know to put 0.5 and 1/(26^2) in the following places:
- Pr[C=ff | M=dd] x Pr[M=dd] = [1/26 x 0.5 + 1/(26^2) x 0.5] x 0.2
- Pr[C=ff | M=de] x Pr[M=de] = [0 x 0.5 + 1/(26^2) x 0.5] x 0.8
I expected the conditional part calculations to be:
- Pr[C=ff | M=dd] = [1/26 x 0.5 + 1/(26) x 0.5]
- Pr[C=ff | M=de] = [0 x 0.5 + 1/(26) x 0.5]
So I would like an "equation" possibly based on the law of total probability and/or Bayes' Theorem (or something which I do not know about), such that I can see the symbolic manipulation/calculations which leads to the simple substitution of values as described above.