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### Course: High school statistics>Unit 6

Lesson 4: Probability from simulations

# Experimental versus theoretical probability simulation

Experimental versus theoretical probability simulation.

## Want to join the conversation?

• do you know the link for this website is?
• Question - Does it matter what the coin side is before the toss is made?
• The side which it is tossed on does NOT matter, because the coin is getting flipped so many times in the air, that it would end up as heads or tails. Speaking in terms from the Law of Large Numbers, a EXTREMELY LARGE amount of flips would probably equal about the theoretical average.
• Logic and truth tables.
Can you please give a brief explanation in connecting to topic to a real world problem or in the work place.
• Probability is our guess or better say estimate of how would things work. A very simple example and realistic could be say there is some chance that say 60% that there will be a traffic jam on a sunday. Say you leave for a fun ride on sunday then it is not necessary that you will encounter a Jam but you can expect it and estimates suggest that there will be a Jam and remember so estimates are just expectation not necessarily we are right. I hope this makes sense and answers our query.
• What's that website called?
• What if I flip the coin three times?
• If you flip the coin three times, there are these possibilities:
1. h, h, h
2. h, h, t
3. h, t, h
4. h, t, t
5. t, h, h
6. t, h, t
7. t, t, h
8, t, t, t

Basically, there are eight outcomes because there are two outcomes for the first flip (heads and tails). As you do more flips, you increase the power which the number of outcomes is raised to.
An equation:
if p = number of outcomes and n = number of times the action is executed,
total probability = p^n
(NOTE: this only works if the events are independent)
• When solving problems in interpreting results of simulations I have no clue as to how to solve them. Mainly reading the charts throws me off.
(1 vote)
• Those are dot plots. Basically, each dot represents one simulation and the number below represents the result of that simulation.

– – –

As an example, I ran 10 simulations of how many times I needed to flip a coin until it landed Heads.

• •
• •
• • • •
1 2 3 4 5

Above the number "1" there are five dots. This means that in five of the simulations it only took one flip for the coin to land Heads.

– – –

Let's say we want to use these simulations to approximate the probability that it takes at least 3 flips for a coin to land Heads.

Probability is the number of favorable outcomes divided by the total number of outcomes.
In this case that would be the number of simulations with 3 or more flips divided by the total number of simulations.

Well, there weren't any simulations with 3 flips,
there was one simulation with 4 flips
and one simulation with 5 flips.
So, there were 0 + 1 + 1 = 2 simulations that needed at least 3 flips.

Also, there were 10 simulations in total.

Thus, the probability that we need at least 3 flips of a coin until it lands Heads is approximately 2∕10 = 0.2
• what happens when you have to experiment and you do several trials and it lands on heads once and lands on tails twice even though you set it up to land on heads more often. Is it possible.
• Yes, this is possible because the probability of getting heads is not 100%. It is only less likely because heads is supposed to come more often and it will as you flip more and more. This is not wrong not is it impossible.
• how does this program generate this toss randomly?