1. Simulating Probabilistic Behaviour
A coin flip
Roll of a fair die
Roll of an unfair die

2. Coin Flip Pie Chart

3. Coin Flip Simulation Generate a series of Random Numbers
Assign a subset of the range of random numbers corresponding to the probability of a result to said result.
Count all the times a random number in within that subset.
Output the Count/Trials
For a random number in [0,1]:
Result
Probability of Result
Assigned Area
Head
0.5
[0,0.5]
Tails
]0.5,1]

4. Rolling a Die
Now we need to have six counters, each with an equal probability of incrementing.
Result
Probability of Result
Assigned Area 1
1/6
[0, ] 2
] ,0.3333] 3
]0.3333,0.5] 4
]0.5, ] 5
] ,0.8333] 6
]0.8333,1]

5. An Unfair Die
The point of this example is to show that any probabilistic event can be simulated with Monte Carlo simulations if we know the probabilities of every result.
Result
Probability of Result
Assigned Area 1 .1
[0,0.1] 2
]0.1,0.2] 3 .2
]0.2,0.4] 4 .3
]0.4,0.7] 5
]0.7,0.9] 6
]0.9,1]

6. Continuous Probability Distributions
There are times when the probability of events occurring are not as obvious as previously shown.

7. How to Proceed
Define an interval along the range of values of the independent variable.
For each interval find the area under the probability distribution function.
Continue as if simulating a rigged die.

8. Gasoline Demand Example
Demand Bin
Probability of Demand
Area Assigned
.03
[0,0.03]
.17
]0.03,0.2]
.47
]0.2,0.67]
.26
]0.67,0.93]
.07
]0.93,1]