PG 289 Question 1

A die is rolled three times. Find the probability that the sum of the outcomes is (a) greater than 9. (b) an odd number.

Utilizing the dice rolling function utilized in discussion 5

dice.sim<- function(n.dice){
  dice <- sample(x = 1:6, size = n.dice, replace = TRUE)
  return(sum(dice))}

n=3
q1a <- (dice.sim(n))/(6^n)
q1a
## [1] 0.06481481

The previous dice function did not work as I thought it would since the value changes every time it runs

q1 <- rep(0,1)
  for (d1 in 1:6)
    for (d2 in 1:6)
      for (d3 in 1:6)
      {s <- d1+d2+d3
      q1[1] <- q1[1]+((s>9))}

(q1a <- q1/6^3)
## [1] 0.625

As to question (b), since dice are only have odd or even values, the probibility is 50% of any roll being odd.