# quesito 1-ii)
urna.1 <- c("ROSSA","ROSSA","ROSSA","BIANCA","BIANCA","BLU")
urna.2 <- c("ROSSA","BIANCA","BIANCA","BLU","BLU","BLU")
prove <- 10000
num <- 0; den <- 0
for (i in 1:prove)
{
    out.1 <- sample(urna.1,size=1,replace=FALSE)
    out.2 <- sample(urna.2,size=1,replace=FALSE)
    den <- den + 1
    if ( (out.1=="ROSSA" & out.2=="ROSSA") |
       (out.1=="BIANCA" & out.2=="BIANCA") |
       (out.1=="BLU" & out.2=="BLU") ) num <- num+1
}

cat(num,den,num/den,"\n")



# quesito 1-iii).
urna.1 <- c("ROSSA","ROSSA","ROSSA","BIANCA","BIANCA","BLU")
urna.2 <- c("ROSSA","BIANCA","BIANCA","BLU","BLU","BLU")
prove <- 10000
num.1 <- 0; num.2 <- 0; den <- 0
for (i in 1:prove)
{
    out.1 <- sample(urna.1,size=1,replace=FALSE)
    out.2 <- sample(urna.2,size=1,replace=FALSE)
    den <- den + 1
    if ((out.1=="ROSSA" & out.2=="ROSSA")) num.1 <- num.1 + 1
    if ((out.1=="BIANCA" & out.2=="BIANCA")) num.2 <- num.2 + 1
}

cat(num.1,num.2,den,num.1/den,num.2/den,"\n")



# quesito 2-i).
urna.1 <- c("ROSSA","ROSSA","ROSSA","BIANCA","BIANCA","BLU")
urna.2 <- c("ROSSA","BIANCA","BIANCA","BLU","BLU","BLU")
urna <- c(urna.1,urna.2)
y <- c("BIANCA","BLU","ROSSA")
prove <- 10000
num <- 0; den <- 0
for (i in 1:prove)
{
    out <- sample(urna,size=3,replace=TRUE)
    den <- den + 1
    ris <- intersect(out,y)
    if (length(ris)==3) num <- num+1
}

cat(num,den,num/den,"\n")



# quesito 2-ii).
urna.1 <- c("ROSSA","ROSSA","ROSSA","BIANCA","BIANCA","BLU")
urna.2 <- c("ROSSA","BIANCA","BIANCA","BLU","BLU","BLU")
urna <- c(urna.1,urna.2)
y <- c("BIANCA","BLU","ROSSA")
prove <- 10000
num <- 0; den <- 0
for (i in 1:prove)
{
    out <- sample(urna,size=3,replace=FALSE)
    den <- den + 1
    ris <- intersect(out,y)
    if (length(ris)==3) num <- num+1
}

cat(num,den,num/den,"\n")