# quesito a)
moneta <- c("Testa","Croce")
nrep <- 100000
nlanci <- 10
x <- sample(moneta,nlanci*nrep,replace=TRUE)
x <- x == "Testa"
x <- matrix(x,nrow=nrep)
p <- apply(x,1,sum)/nlanci*100
euro <- ifelse(p>60,100,0)
mean(euro)

nlanci <- 100
x <- sample(moneta,nlanci*nrep,replace=TRUE)
x <- x == "Testa"
x <- matrix(x,nrow=nrep)
p <- apply(x,1,sum)/nlanci*100
euro <- ifelse(p>60,100,0)
mean(euro)


# quesito b)
moneta <- c("Testa","Croce")
nrep <- 100000
nlanci <- 10
x <- sample(moneta,nlanci*nrep,replace=TRUE)
x <- x == "Testa"
x <- matrix(x,nrow=nrep)
p <- apply(x,1,sum)/nlanci*100
euro <- ifelse(p>40,100,0)
mean(euro)

nlanci <- 100
x <- sample(moneta,nlanci*nrep,replace=TRUE)
x <- x == "Testa"
x <- matrix(x,nrow=nrep)
p <- apply(x,1,sum)/nlanci*100
euro <- ifelse(p>40,100,0)
mean(euro)


# quesito c)
moneta <- c("Testa","Croce")
nrep <- 100000
nlanci <- 10
x <- sample(moneta,nlanci*nrep,replace=TRUE)
x <- x == "Testa"
x <- matrix(x,nrow=nrep)
p <- apply(x,1,sum)/nlanci*100
euro <- ifelse((p>40 & p<60),100,0)
mean(euro)

nlanci <- 100
x <- sample(moneta,nlanci*nrep,replace=TRUE)
x <- x == "Testa"
x <- matrix(x,nrow=nrep)
p <- apply(x,1,sum)/nlanci*100
euro <- ifelse((p>40 & p<60),100,0)
mean(euro)


# quesito d)
moneta <- c("Testa","Croce")
nrep <- 100000
nlanci <- 10
x <- sample(moneta,nlanci*nrep,replace=TRUE)
x <- x == "Testa"
x <- matrix(x,nrow=nrep)
p <- apply(x,1,sum)/nlanci*100
euro <- ifelse((p == 50),100,0)
mean(euro)

nlanci <- 100
x <- sample(moneta,nlanci*nrep,replace=TRUE)
x <- x == "Testa"
x <- matrix(x,nrow=nrep)
p <- apply(x,1,sum)/nlanci*100
euro <- ifelse((p == 50),100,0)
mean(euro)