Objetivo

Calcular probabilidades con operaciones de conjutno

Desarrollo

Inicializar conjuntos

V=c("Gael", "Emilio", "Daniela","Marco", "Sebastian", "Juan", "Paty", "Carlos")
T=c("Ruben"," Fanny","Aracely","Marco","Juan", "Carlos")
B=c("Gael","Daniela","Marco","Sebastian","Emilio")
A=c("Emilio","Ruben","Sebastian")
Te=c("Fanny", "Marco","Oscar","Luis","Lucy","Mary")
R=c("Hugo","Roberto","Yarely","Lucy","Carlos")

Mostrar todos los conjuntos

V; T; B; A; Te; R
## [1] "Gael"      "Emilio"    "Daniela"   "Marco"     "Sebastian" "Juan"     
## [7] "Paty"      "Carlos"
## [1] "Ruben"   " Fanny"  "Aracely" "Marco"   "Juan"    "Carlos"
## [1] "Gael"      "Daniela"   "Marco"     "Sebastian" "Emilio"
## [1] "Emilio"    "Ruben"     "Sebastian"
## [1] "Fanny" "Marco" "Oscar" "Luis"  "Lucy"  "Mary"
## [1] "Hugo"    "Roberto" "Yarely"  "Lucy"    "Carlos"

Crear todo el espacio muestral con la union de todos los conjuntos

union(union(union(union(union(V,T),B),A),Te),R)
##  [1] "Gael"      "Emilio"    "Daniela"   "Marco"     "Sebastian" "Juan"     
##  [7] "Paty"      "Carlos"    "Ruben"     " Fanny"    "Aracely"   "Fanny"    
## [13] "Oscar"     "Luis"      "Lucy"      "Mary"      "Hugo"      "Roberto"  
## [19] "Yarely"
S_espacio=union(union(union(union(union(V,T),B),A),Te),R)
S_espacio
##  [1] "Gael"      "Emilio"    "Daniela"   "Marco"     "Sebastian" "Juan"     
##  [7] "Paty"      "Carlos"    "Ruben"     " Fanny"    "Aracely"   "Fanny"    
## [13] "Oscar"     "Luis"      "Lucy"      "Mary"      "Hugo"      "Roberto"  
## [19] "Yarely"
n=length(S_espacio)

Cual es la probabilidad de union Voley y Ajedrez

VUA=union(V,A)
VUA
## [1] "Gael"      "Emilio"    "Daniela"   "Marco"     "Sebastian" "Juan"     
## [7] "Paty"      "Carlos"    "Ruben"
prob=length(VUA) / n*100
paste(prob,"%")
## [1] "47.3684210526316 %"

Cual es la probabilida de interseccion Tenis y Rondalla

TeIR=intersect(Te,R)
TeIR
## [1] "Lucy"
prob=length(TeIR) / n*100
paste(prob,"%")
## [1] "5.26315789473684 %"

Cual es la probabilidad de voley menos basquet

V_menos_B=setdiff(V,B)
V_menos_B
## [1] "Juan"   "Paty"   "Carlos"
prob=length(V_menos_B) / n*100
paste(prob,"%")
## [1] "15.7894736842105 %"

Cual es la probabilidad de basquet menos voley

B_menos_V=setdiff(B,V)
B_menos_V
## character(0)
prob=length(B_menos_V) / n*100
paste(prob,"%")
## [1] "0 %"

Cual es la probabilidad del complemento del teatro

Cual es la probabilidad de delegi a una persona que no participe en teatro

T_complemento=setdiff(S_espacio,T)
T_complemento
##  [1] "Gael"      "Emilio"    "Daniela"   "Sebastian" "Paty"      "Fanny"    
##  [7] "Oscar"     "Luis"      "Lucy"      "Mary"      "Hugo"      "Roberto"  
## [13] "Yarely"
prob=length(T_complemento) / n*100
paste(prob,"%")
## [1] "68.4210526315789 %"