# Probability problem

This is a problem set. Some of these are easy, others are far more difficult. The purpose of these problems sets are:

- to build your skill applying computational thinking to a problem
- to assess your knowledge and skills of different programming practices

## Contents

## What is this problem set trying to do[edit]

We are working with iteration and selection here.

## The Problem[edit]

I found this problem on the daily coding problem. It's a great place to find fun problems to practice your programming skills.

Alice wants to join her school's Probability Student Club. Membership dues are computed via one of two simple probabilistic games.

The first game: roll a die repeatedly. Stop rolling once you get a five followed by a six. Your number of rolls is the amount you pay, in dollars.

The second game: same, except that the stopping condition is a five followed by a five.

Which of the two games should Alice elect to play? Does it even matter?

Construct a program to simulate the two games and calculate their expected value. You should construct the program so it runs several thousand (10,000) iterations of each method and compares the results.

## How you will be assessed[edit]

Your solution will be graded using the following axis:

**Scope**

- To what extent does your code implement the features required by our specification?
- To what extent is there evidence of effort?

**Correctness**

- To what extent did your code meet specifications?
- To what extent did your code meet unit tests?
- To what extent is your code free of bugs?

**Design**

- To what extent is your code written well (i.e. clearly, efficiently, elegantly, and/or logically)?
- To what extent is your code eliminating repetition?
- To what extent is your code using functions appropriately?

**Style**

- To what extent is your code readable?
- To what extent is your code commented?
- To what extent are your variables well named?
- To what extent do you adhere to style guide?

## References[edit]

## A possible solution[edit]

Click the expand link to see one possible solution, but NOT before you have tried and failed!

```
# Thank you to Patrick, an awesome 11th grade student in the year 2020!!!
#
#
import random
import os
os.system("clear")
# game 1
def game1(RunAmount):
AmountWon = 0
for x in range(RunAmount):
dicegame1 = random.randint(1, 6)
if dicegame1 == 5:
dicegame11 = random.randint(1, 6)
if dicegame11 == 5:
AmountWon = AmountWon + 1
else:
continue
return AmountWon
# game 2
def game2(RunAmount):
AmountWon2 = 0
for x in range(RunAmount):
dicegame1 = random.randint(1, 6)
if dicegame1 == 5:
dicegame11 = random.randint(1, 6)
if dicegame11 == 6:
AmountWon2 = AmountWon2 + 1
else:
continue
return AmountWon2
game1RunAmount = int(input("Run game 1 how many times? "))
game2RunAmount = int(input("Run game 2 how many times? "))
amountOfDouble5 = (game1(game1RunAmount))
amountOf56 = (game2(game2RunAmount))
print(amountOfDouble5, "Double 5's out of ", game1RunAmount,
" rolls which means Alice has to pay", amountOfDouble5, '$')
print(amountOf56, "5's then 6's out of ", game2RunAmount,
" rolls which means Alice has to pay", amountOf56, '$')
if amountOfDouble5 > amountOf56:
print("Alice should play game 2")
elif amountOfDouble5 < amountOf56:
print("Alice should play game 1")
```

A unit of abstract mathematical system subject to the laws of arithmetic.

Develop information in a diagrammatic or logical form.

Obtain a numerical answer showing the relevant stages in the working.

Develop information in a diagrammatic or logical form.

Consider the merits or otherwise of an argument or concept. Opinions and conclusions should be presented clearly and supported with appropriate evidence and sound argument.

Produce a plan, simulation or model.