proportion$\_$win

iv$.$ What value does the proportion of wins move towards as the number of games played

increases? How does this value compare to the probability of winning? $[3]$

flongrightarrow

v$.$ Use the R codes below to plot a graph that shows how the proportion of wins changed

as more games are played. $[6]*$attached to submission

# create data

number$\_$of$\_$games

$c(100,200,300,400,500,600,700,800,900,1000)$

Probability

data data.frame$($number$\_$of$\_$games, probability$)$

# usual line chart

plot$($probability number$\_$of$\_$games, data, type $="1",$

col$=$c$("$steelblue$","$#$69$b$3$a$2"),$ lwd$=2)$ Guided Investigation Chapter $P$

Tetrahedral Dice

A game involves tossing two tetrahedral dice, where if a pair is obtained, i$.$e$.,$ a pair of $1s$ or a

pair of $2s$ etc., the game is won.

i$.$ Complete the following table to show all possible outcomes if two tetrahedral dice is

tossed. $[8]$

ii$.$ What is the probability of winning the game? Describe what the probability is in this

instance. $[3]$

$25\%$ probability of winning, rolling a pair

iii. Use the following $R$ codes below to determine the proportion of wins given the

increasing number of games played and complete the table that follows. $[10]$

j

#Create a vector of possible results, $1$ is a win and $0$

#is a loss.

outcome$\_$vector

#Sample with replacement

numberOfGames

sampled vector sample $($outcome vector, size $=$

numberofGames, replace $=$ TRUE$)$

proportion$\_$winsum$($sampled$\_$vector$)/$numberofGames