# Tossing Coins and Rolling Dice

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```							                                                                                                Order + Chaos
Basic Probability

Tossing Coins and Rolling Dice
Open the spread sheet “Coins”. Look at the tab labelled “One Coin”. It simulates the tossing of a single coin 1000
times.
What are the possible outcomes for tossing one coin?

How many times does a Head occur?

Press the F9 button to refresh the data and simulate another 1000 tosses.
Now how many times does a Head occur?

Repeat this three times so that you can fill the table below.

1

2

3

4

5

Average

The percentage that you have obtained is the experimental probability of obtaining a Head.

The theoretical probability is what would be achieved with an infinite number of tosses. What is the theoretical
probability of getting a Head when a coin is tossed?

Now look at the tab labelled “Two Coins”. It simulates the tossing of two coins 1000 times.
What are all the possible outcomes for tossing two coins?
Order + Chaos
Basic Probability
How many times does a Head and a Tail occur in any order?

Press the F9 button to refresh the data and simulate another 1000 tosses.
Now how many times does a Head and a Tail occur?

Repeat this three times so that you can fill the table below.

Simulation        No. of HT’s      Percentage HT’s

1

2

3

4

5

Average

Again the percentage that you have obtained is the experimental probability of obtaining a Head and a Tail.

What is the theoretical probability of getting a Head on one coin and a Tail on the other?

Now look at the tab labelled “Three Coins”. It simulates the tossing of three coins 1000 times.
What are all the possible outcomes for tossing three coins?

List all the ways that you can get two Heads when you toss three coins?
Order + Chaos
Basic Probability
How many times do two Heads occur in any order in the 1000 tosses?

Press the F9 button to refresh the data and simulate another 1000 tosses.
Now how many times do two Heads occur?

Repeat this three times so that you can fill the table below.

No. of two      Percentage of two
Simulation
1

2

3

4

5

Average

What is the theoretical probability of getting two Heads?

What is the theoretical probability of getting two Tails?

What is the theoretical probability of getting at least one Head?

Now look at the tab labelled “Five Coins”. It simulates the tossing of (surprise, surprise) five coins 1000 times.
What are all the possible outcomes for tossing five coins?
Order + Chaos
Basic Probability
List all the ways that you can get two Heads when you toss five coins?

How many times do two Heads occur in any order in the 1000 tosses?

Press the F9 button to refresh the data and simulate another 1000 tosses.
Now how many times do two Heads occur?

Repeat this three times so that you can fill the table below.

No. of two     Percentage of two
Simulation
1

2

3

4

5

Average

What is the theoretical probability of getting two Heads?

What is the theoretical probability of getting two Tails?

What is the theoretical probability of getting at least one Head?
Order + Chaos
Basic Probability
Now open the spread sheet “Dice”. Look at the tab labelled “One Die”. It simulates the rolling of a single die 1000
times.
What are the possible outcomes for rolling one die?

How many times does a 5 occur?

Press the F9 button to refresh the data and simulate another 1000 tosses.
Now how many times does a 5 occur?

Repeat this three times so that you can fill the table below.

Simulation          No. of 5’       Percentage 5’s

1

2

3

4

5

Average

The percentage that you have obtained is the experimental probability of obtaining a 5.

The theoretical probability is what would be achieved with an infinite number of tosses. What is the theoretical
probability of getting a 5 when a die is rolled?

Now look at the tab labelled “Two Dice”. It simulates the rolling of two dice 1000 times.
What are all the possible outcomes for rolling two dice?

If the results on each die are added together, what are the possible totals when rolling two dice?
Order + Chaos
Basic Probability
How many times does a total of 5 occur?

Press the F9 button to refresh the data and simulate another 1000 tosses.
Now how many times does a total of 5 occur?

Repeat this three times so that you can fill the table below.

Simulation          No. of 5’s     Percentage 5’s

1

2

3

4

5

Average

Again the percentage that you have obtained is the experimental probability of obtaining a total of 5.

What is the theoretical probability of getting a total of 5?

The graph is a bar graph showing the numbers of each possible outcome in the 1000 rolls. How would you describe
the shape of the graph?

Now look at the tab labelled “Three Dice”. It simulates the tossing of three dice 1000 times.
What are all the possible outcomes for rolling three dice? (there are 216 of them so assume that 1, 2, 3 is the same as
3, 2, 1
Order + Chaos
Basic Probability
List all the ways that you can get a total of 12 when you roll three dice?

Press the F9 button to refresh the data and simulate another 1000 rolls.
Now how many times does a total of 12 occur?

Repeat this three times so that you can fill the table below.

Simulation        No. of 12’s        Percentage of 12’s

1

2

3

4

5

Average

What is the theoretical probability of getting a total of 12?

What is the theoretical probability of getting a total of 15?

What is the theoretical probability of getting a total of at least 10?

The graph again shows the numbers of each possible outcome in the 1000 rolls. How would you describe the shape
of the graph? Is it any different than the previous one?
Order + Chaos
Basic Probability
Now look at the tab labelled “Five Dice”. It simulates the rolling of five dice 1000 times.
What are all the possible outcomes for rolling five dice that contain at least one 1? Again ignore order.

List all the ways that you can get a total of 20 when you roll five dice?

How many times does a total of 20 occur in the 1000 rolls?

Press the F9 button to refresh the data and simulate another 1000 tosses.
Now how many times does a total of 20 occur?

Repeat this three times so that you can fill the table below.

Simulation         No. of 20’s      Percentage of 20’s

1

2

3

4

5

Average

What is the theoretical probability of getting a total of 20?

What is the theoretical probability of getting a total less than 10?
Order + Chaos
Basic Probability
The graph again shows the numbers of each possible outcome in the 1000 rolls. How would you describe the shape
of the graph? Is it any different than the previous ones?

Now look at the tab labelled “Five with More”. It simulates the rolling of five dice 10000 times.
The graph again shows the numbers of each possible outcome in the 1000 rolls. How would you describe the shape
of the graph? Is it any different than the previous ones?

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