Some Applications of Bayes' Rule in Probability Theory to Electrocatalytic Reaction Engineering

Table 4

Probabilities of flawlessness/defectiveness expected from an EC tester (Application No. 3).

Event	Bayes’ rule	Event probability
EC tested defective, but found flawless	𝑃(𝐴^′/𝐵)=𝑃(𝐵/𝐴^′)𝑃(𝐴^′)𝑃(𝐵/𝐴^′)𝑃(𝐴^′)+𝑃(𝐵/𝐴)𝑃(𝐴)	0.1983
EC tested flawless, and found flawless	𝑃(𝐴^′/𝐵^′)=𝑃(𝐵^′/𝐴^′)𝑃(𝐴^′)𝑃(𝐵^′/𝐴^′)𝑃(𝐴^′)+𝑃(𝐵^′/𝐴)𝑃(𝐴)	0.9987
EC tested flawless, but found defective	𝑃(𝐴/𝐵^′)=𝑃(𝐵^′/𝐴)𝑃(𝐴)𝑃(𝐵^′/𝐴)𝑃(𝐴)+𝑃(𝐵^′/𝐴^′)𝑃(𝐴^′)	0.0013
EC tested defective, and found defective	𝑃(𝐴/𝐵)=𝑃(𝐵/𝐴)𝑃(𝐴)𝑃(𝐵/𝐴)𝑃(𝐴)+𝑃(𝐵/𝐴^′)𝑃(𝐴^′)	0.8017

P(A/B′) + P(A′/B′) = P(A/B) + P(A′/B) = 1; P(A) = 0.04; P(A′) = 1 − 0.04 = 0.96.