## Captain Walter Fried's Fish Notes Annex to #F 71, Screed on Delta D Counts and Colossus runs## Page 11 |
Tony Sale's Codes and Ciphers |

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- Appendix p1

- A run has been done for X12 giving a result. "This result is correct"

- A second run, using the result of the X12 run, has been done for X34,

scores were obtained we call z, and the statement "the highest score in

this run gives the correct setting" we call B.

- P(X,Y) means "the probability of X given Y",

O(X,Y) means "the odds on X given Y",

nA means "not A"

- (1) P(X,Y).P(Y) = P(X&Y)

the second run to find O(B, Z&A) = o.

(AES Note: I have used "d" in place of lower case Greek Delta, "e" in place of

epsilon and "m" in place of )

- Let P(z,A) = d(1+o), P(z & nB, nA) = d' , P(z, nA) = d'(1+)

- P(Z & B, A) = od

P(Z & nB, A) = d

- P(Z & B, nA) = ed'

P(Z & nB, nA) = d'

- P(Z) = P(Z & nA) + P(Z & A)

= P(Z, nA).P(A) + P(Z ,A)P(A)

= d(1+e)(1-p) + d(1+o)p

- P(A & B,Z) = P(A & B & Z)/P(Z)

- = P(Z & B, A).P(A) / P(Z)

= pod/P(Z)

- O(A & B, Z) = pod/P(Z) - pod

- = pod/d'(1+e)(1-p) + dp