What are simulations by College Board definition?

Simulations are abstractions that mimic more complex objects or phenomena from the real world
- Purposes include drawing inferences without the contraints of the real world
Simulations use varying sets of values to reflect the changing state of a real phenomenon
Often, when developing a simulation, it is necessary to remove specific details or simplify aspects
- Simulations can often contain bias based on which details or real-world elements were included/excluded
Simulations allow the formulation of hypotheses under consideration
Variability and randomness of the world is considered using random number generators
Examples: rolling dice, spinners, molecular models, analyze chemicals/reactions...

Functions that are often needed

import random # a module that defines a series of functions for generating or manipulating random integers
random.choice() #returns a randomly selected element from the specified sequence
random.choice(mylist) # returns random value from list
random.randint(0,10) #randomly selects an integer from given range; range in this case is from 0 to 10
random.random() #will generate a random float between 0.0 to 1.

Examples of College Board MC Simulation Questions

Question: The following code simulates the feeding of 4 fish in an aquarium while the owner is on a 5-day trip:

numFish ← 4

foodPerDay ← 20

foodLeft ← 160

daysStarving ← 0

REPEAT 5 TIMES {

foodConsumed ← numFish * foodPerDay

foodLeft ← foodLeft - foodConsumed

IF (foodLeft < 0) {

daysStarving ← daysStarving + 1

}

}

This simulation simplifies a real-world scenario into something that can be modeled in code and executed on a computer.

Simulation Code Starters

Pull random card from a deck

Additions we would make to this include:
- Visual of the card chosen
- User can choose how many cards should be chosen

import random

cards = ["Ace", "2", "3", "4", "5", "6", "7", "8", "9", "10", "Jack", "Queen", "King"] 
suits = ["Diamonds", "Hearts", "Spades", "Clubs"]

print(random.choice(cards) + " of " + random.choice(suits))

2 of Clubs

Frog jumping

Additions
- Again, add visuals of the frog
- Add more variables to make this more realistic
  - Weather: If the weather is worse---> frog should jump less
  - Time: If it is day time ---> frog should jump less
  - ^ These could be user inputs

import random
length = [0, 1, 2, 3, 4, 5]
direction = ["left", "right"]

print("The frog jumped" , random.choice(length) , "hops to the" , random.choice(direction))

The frog jumped 5 hops to the left

Population after natural disaster

When natural disasters occur, certain times random traits are wiped from a population
- Take for example the Galapagos finches
  - When a drought hit, smaller seeds became more rare so finches with larger beaks had greater chance of survival
  - this can be modeled (with lots of simplification)
Additions we would add
- specific data on beak size/wing length/height
  - so for certain disaster, wing legnths > 5.5 survived

import random

beak =  ["small-beak", "long-beak", "medium-beak"],
wing = ["small-wings", "large-wings", "medium-wings"],
height = ["short", "tall","medium"]


naturaldisaster = ["flood", "drought", "fire", "hurricane", "dustbowl"]


print("When a" , random.choice(naturaldisaster) , "hit",  random.choice(height), "birds died")

When a drought hit short birds died