P (A∩B) == P (A) ·P (B | A)

P (B | A) == (P (A∩B))/(P (A))

P (A∩B∩C) == P (A) ·P (B | A) ·P (C | A∩B)

P (A) == P (A_1) ·P (A | A_1) + P (A_2) ·P (A | A_2)

P (A_k | A) == (P (A_k) ·P (A | A_k))/(Underoverscript[∑, j = 1, arg3] P (A_j) ·P (A | A_j))

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Grasp Period Probabilty

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D - a (high), b (low), a + b (period)

R - c (high), d (low), c + d (period)

P (D) = (D 인식)/D주기, P (D^′) = (D 불인식)/D주기

P (R) = (R 인식)/R주기, P (R^′) = (R 불인식)/R주기

P (D | R) = R환경 (D 인식)/R주기, P (D^′ | R) = R환경 (D 불인식)/R주기

P (R | D) = D환경 (R 인식)/D주기, P (R^′ | D) = D환경 (R 불인식)/D주기

P (D) = b/(a + b), P (D^′) = a/(a + b)

P (R) = d/(c + d), P (R^′) = c/(c + d)

P (D | R) = (d - a)/(c + d), P (D^′ | R) = (c + a)/(c + d)

P (R | D) = (b - c)/(a + b), P (R^′ | D) = (a + c)/(a + b)

P (e) = P (D) ·P (R^′ | D) + P (R) ·P (D^′ | R)

= P (D∩R^′) + P (R∩D^′)

= (a + c) (b/(a + b)^2 + d/(c + d)^2)

예

a = 16 ;

b = 132 ;

c = 59 ;

d = 48 ;

(a + c) (b /(a + b)^2 + ( d)/(c + d)^2)//N

0.76641

오류확률

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전체 경우 : U 주기와 V 주기의 공배수

P (U) = (a (c + d))/((a + b) (c + d))

P (e | U) = ((a + c) (a + b))/((a + b) (c + d))

P (V) = (c (a + b))/((a + b) (c + d))

P (e | V) = ((a + c) (c + d))/((a + b) (c + d))

P (e) = P (e | U) P (U) + P (e | V) P (V)

예