Gain experience using NumPy arrays to solve problems. In a modified game of Yahtzee, five eight$-$sided dice are rolled once.

For this assignment, you will simulate this modified game of Yahtzee to determine how likely certain outcomes are.

In this modified version of Yahtzee, a Low Roll occurs when each of the five dice is either a $1$ or an $2.$ For example, $1-1-1-1-1$ or $2-2-1-2-1.$

In this modified version of Yahtzee, a Three of a Kind occurs when three of the dice show the same number. The other two dice must not show this number and must also be different from one another. For example, $4-7-4-4-2$ but not $4-7-4-4-7.$

In this modified version of Yahtzee, a Large Straight occurs when the five numbers can be arranged consecutively $($for example, $1-3-4-2-5$ or $5-7-4-6-3).$ Hint: the numpy library contains a sort function. In the section called Class and function definitions, add the missing methods such that when the main is called, it might produce the following output. You will need to write new code, but do not change any of the existing code.

Number of Rolls: $20000$

$---------------------$

Number of Low Rolls: $18$

Percent: $0\mathrm{.}09\%$

Number of Three of a Kinds: $1995$

Percent: $9\mathrm{.}97\%$

Number of Large Straights: $261$

Percent: $1\mathrm{.}30\%$

Yahtzee code:

import numpy as np

import random

class Die:

def $\_\_$init$\_\_($self$,$ sides$)$:

$"""$A constructor method to create a die"""

self.sides $=$ sides

def roll$($self$)$:

$"""$A general method to roll the die"""

return random.randint$(1,$ self.sides$)$

class Yahtzee:

def $\_\_$init$\_\_($self$,$ sides$)$:

$"""$A constructor method that can record $5$ dice rolls"""

self.rolls $=$ np$.$zeros$(5,$ dtype$=$np$.$int$16)$

self.sides $=$ sides

def roll$\_$dice$($self$)$:

$"""$A general method that rolls $5$ dice"""

for i in range$($len$($self$.$rolls$))$:

self.rolls$[$i$]=$ Die$($self$.$sides$).$roll$()$

def count$\_$outcomes$($self$)$:

$"""$A helper method that determines how many $1$s$,2$s$,$ etc. were rolled"""

counts $=$ np$.$zeros$($self$.$sides $+1,$ dtype$=$np$.$int$16)$

for roll in self.rolls:

counts$[$roll$]+=1$

return counts

def main$($how$\_$many$)$:

low$\_$rolls $=0$

three$\_$of$\_$a$\_$kinds $=0$

large$\_$straights $=0$

game $=$ Yahtzee$(8)$ # $8-$sided dice

for i in range$($how$\_$many$)$:

game.roll$\_$dice$()$

if game.is$\_$it$\_$low$\_$roll$()$:

low$\_$rolls $+=1$

elif game.is$\_$it$\_$three$\_$of$\_$a$\_$kind$()$:

three$\_$of$\_$a$\_$kinds $+=1$

elif game.is$\_$it$\_$large$\_$straight$()$:

large$\_$straights $+=1$

print$("$Number of Rolls:", how$\_$many$)$

print$("---------------------")$

print$("$Number of Low Rolls:", low$\_$rolls$)$

print$("$Percent:$","\{$:$\mathrm{.}2$f$\}\%$

$".$format$($low$\_$rolls $*100/$ how$\_$many$))$

print$("$Number of Three of a Kinds:", three$\_$of$\_$a$\_$kinds$)$

print$("$Percent:$","\{$:$\mathrm{.}2$f$\}\%$

$".$format$($three$\_$of$\_$a$\_$kinds $*100/$ how$\_$many$))$

print$("$Number of Large Straights:", large$\_$straights$)$

print$("$Percent:$","\{$:$\mathrm{.}2$f$\}\%".$format$($large$\_$straights $*100/$ how$\_$many$))$

n $=10000$

main$($n$)$