EVENTOS

1. C= Tiene cuentas de ahorro CDT= tiene CDT

C'= No tiene cuentas de ahorro CDT'= No tiene CDT

P (C)= 0.65

P (C ∩CDT)= 0.30

P ( CDT/C) = P (CDT ∩C) / P (C)

= 0.30 / 0.65

= 46%

2. B= Localizada en Bogotá M= Localizada en Medellín

B'= No localizada en Bogotá M'= No localizada en Medellín

P (B)= 0.33

P (M)= 0.26

P (B U M) = 0.51

P (B U M) = P (B)+ P (M) - P (B ∩M)

P ( B U M) - P (B) - P (M) = -P (B ∩M)

0.51 -0.3 - 0.26 = -P (B ∩M)

-0.08 = -P (B ∩M)

0.08 = P (B ∩M)

P (B' ∩M') = 0.49 ~ 49%

3. A B C Total

D 0.05 0.10 0.15 0.30

I 0.35 0.25 0.10 0.70

Total 0.40 0.0.34 0.25 1

a. P (C/I) = P (C ∩I)/ P (I) = 0.10 /0.70 = 14%

b. P (D ∩A)= P (D ∩A)/P (A) = 0.50/0.40 = 12.5%

c. P (B/D) + (C/D)

P (B U C/D) = P [(B U C) ∩D]/ P(D)

P[(B ∩D) + P (C ∩D)]/ P(D)

= 0.10 + 0.15/0.30 = 0.25/0.30 = 83.3%

P (B ∩D)/ P(D) + P (C ∩B)/ P(D)

=0.10/0.30 + 0.15/0.30

=0.10+0.15/0.30

=0.25/0.30 = 83.3%

● P (C U I)= P(C) + P(I) - P(C ∩I)

=0.25 + 0.70 - 0.10

= 0.85 ~ 85%

4. P(A)= 0.32

P(B)= 0.28

P(A AB)= 0.12

A A ' Total

B 0.12 0.16 0.28

B' 0.20 0.52 0.72

Total 0.32 0.68 1

a. P(A') = 0.68

b. P(A' ∩B) = 0.16

P(A' ∩B) = P(B)- P(A ∩B)

= 0.28- 0.12 = 0.16

c. P(A U B)= P (A) + P (B) - P (A ∩B)

=0.32 + 0.28 - 0.12

=0.48 ~ 48%

d. P (A ∩B')= 0.20

e. P(A U B)'= 1-0.48

= 0.52~ 52%

f. P (A' U B) = P (A')+P (B) - P (A' ∩ B)

= 0.68 + 0,28 - 0.16

=0.80 ~ 80%

A= Se cierra EPS Armenia

A'=No se cierre EPS Armenia

P= Se cierre EPS Pereira

P'= No se cierre EPS Pereira

P (A)= 0.48

P (B)= 0.36

P (A U P)= 0.625

P (A ∩B)= 0.215

A A'

P 0.215 0.145 0.36

P' 0.265 0.375 0.64

0.480 0.52 1

P (A U P)= P (A) + P (P) - P (A ∩P)

P (A U P) - P (A) - P(P) = - P (A ∩P)

0.625 - 0.48 - 0.36= - P (A ∩P)

- 0.215 = - P (A ∩P)

0,215= P (A ∩P)

P(A' ∩P') = 0.375 ~ 37.5 %