## Exercises - Simulation in R

1. Simulate the number of games won after playing a game 10,000 times when the probability of a win on any game played is $0.30$.

> data=runif(10000,0,1)
> wins=data[data < 0.30]
> length(wins)
[1] 3035


2. Simulate a sequence of letters "R", "B", and "W" corresponding to a possible order of colors seen when randomly arranging in a sequence all of the marbles found in a bag containing $4$ red marbles, $4$ blue marbles, and $2$ white marbles, such as the one shown below.

 "W" "B" "W" "B" "R" "R" "B" "B" "R" "R"

  bag.of.marbles = c(rep("R",4),rep("B",4),rep("W",2))
sample(bag.of.marbles,length(bag.of.marbles),replace=FALSE)

3. Simulate a randomly drawn hand of five cards taken from a standard deck (without replacement), with a vector of strings of text similar to what is shown below, where each card is a string that indicates the rank (A, 2-10, J, Q, or K) and suit (H, D, C, or S) as the sample output below suggests.

"9 H" "K H" "Q D" "3 D" "5 C"

> suits = c("H","D","C","S")
> ranks = c("A",paste(2:10),"J","Q","K")
> deck = paste(rep(ranks,4),rep(suits,each=13))
> sample(deck,5,replace=FALSE)

4. Simulate with a vector like the one shown below, $10$ sums of random rolls of $4$ standard dice.

13 14 19 22 13 15 18 13 14 19

  replicate(10, sum(sample(1:6, size=4, replace=TRUE))