A tree diagram or table shows the possibilities. The traditional tree diagram is
incorporated into the following chart. A tree diagram will include the possibilities
and the branches, while the chart illustrates the same possibilities without the branches.
Method 1: Tree Diagram
Roll Die 1 until you get 1, then look at the charts between the two
dice. Roll Die 2. It will display the value from 1 to 6.
Each possibility for Die 1 connects with the six possibilities for
Die 2. There are 36 possibile outcomes when you roll two dice.
Event
A: Die Toss
1
1
2
3
4
5
6
2
1
2
3
4
5
6
3
1
2
3
4
5
6
4
1
2
3
4
5
6
5
1
2
3
4
5
6
6
1
2
3
4
5
6
Event
B: Die Toss
Method 2: Table
The virtual spreadsheet below has been started for you. Complete the spreadsheet
to show the 36 possibilities for 2 six-sided dice thrown. Click on the Check
button to confirm your solution.
The number of times each event occurs on the the tree diagram or
table.
0
1
2
3
4
5
6
5
4
3
2
1
Total possible outcomes
36
3636
36
36
36
36
36
36
36
36
36
36
Theoretical probability for each sum
0/36
1/36
2/36
3/36
4/36
5/36
6/36
5/36
4/36
3/36
2/36
1/36
Two Coins
Event
A: Coin 1 Flip
Event
B: Coin 2 Flip
Method 1: Tree Diagram
There are 4 possible outcomes when you flip two coins. The table
below shows the same possibilities, but does not include the branches connecting each
possibility for Coin 1 with the two possibilities for Coin 2.
Coin 1
Coin 2
H
H
T
T
H
T
Method 2: Table
Make a chart to show the 4 possibilities for 2 coins. Click on the Check
button to confirm your solution?
A Coin and Six-sided Die
Event
A: Coin Flip
Event
B: Die Toss
Method 1
Complete the tree diagram to show all of the possible outcomes of flipping
a coin and tossing a die. Compare it to the table below. It should show the
same possiblilities, but will include branches connecting each possibility for Die
with the two possibilities for Coin. There are 12 possible outcomes when
you roll a die and flip a coin.
Die
Coin
1
H
T
2
H
T
3
H
T
4
H
T
5
H
T
6
H
T
Method 2
Make a chart to show the 12 possibilities for a coin and six-sided
die tossed. Click on the Check button to confirm your solution.
A 5 Sector Spinner and Coin
Event
A: Spin Wheel
Event B:
Coin Flip
Complete the tree diagram to show all of the
possible outcomes of flipping a coin and spinning a 5 sector spinner. Compare it to
the table below. It should show the same possiblilities, but will include branches
connecting each possibility for Spinner with
the two possibilities for Coin. There are 10
possible outcomes when you spin a 5 sector spinner and flip a coin.
Spinner
Coin
green
H
T
blue
H
T
white
H
T
grey
H
T
red
H
T
number of possible outcomes = 5
x 2 = 10
Remember when there are two independent events, the number of possible outcomes
equals the number of possible outcomes of the first event times the possible outcomes of
the second event.
Coin and 4 Sector Spinner
Make a chart to show the 8 possibilities for a coin and four sector
spinner (blue, green, cyan, magenta)? Click on the Check
button to confirm your solution.
Toss one six-sided dice and spin
a five sector color spinner. What is the theoretical probability of a particular
number and color being selected?
Solution:
You can use a real die and spinner or use the virtual ones above.
The probability of of any number being tossed is 1/6, while the probability of the spinner
stopping on each color is 1/5. Refer to the probability of the sum of two dice tossed if
necessary. Examples:
P(5, green) means the probability of tossing
5 and spinning green
P(3, red) means the probability of tossing 3
and spinning red
Complete 30 trials and complete the experimental
probability.
Two Events
Experimental
Probability
Theoretical Probability
P(5, green) =
/30
1/6 x 1/5 = 1/30 = 0.0333... =
3.3%
P(3, blue) =
/30
1/6 x 1/5 = 1/30 = 0.0333... =
3.3%
Probability
of Rolling Dice and Spinning a Colour
Event
A: Toss Dice
Event
B: Spin Wheel
Toss two six-sided die and spin a five sector color
spinner. What is the probability of a particular number and color being selected?
Solution:
You can use real dice and spinner or use the virtual ones. The
probability of of any number being tossed is 1/6, while the probability of the spinner
stopping on each color is 1/5. Examples:
P(5, green) means the probability of tossing
5 and spinning green
P(3, red) means the probability of tossing 3
and spinning red
Complete 180 trials and complete the experimental probability.
Two Events
Experimental Probability
Theoretical Probability
P(5, green) =
/180
4/36 x 1/5 = 4/180 = 0.0222... =
2.2%
P(3, red) =
/180
2/36 x 1/5 = 2/180 = 0.0111... =
1.1%
Probability of
Drawing Two Cards
To be independent, you must put the first card back, before drawing the
second. This is equivalent to drawing from two different decks of cards.
Complete the appropriate number of trials and complete the experimental
probability.
This game is known under many names,
"Concentration" for example. Click on two boxes, if they match, they remain
showing. When all images show, the game is over. The challenge is to finish in as few
moves as possible.
What is the probability of getting a pair on the first two selections?
How would the probability change
if the person did not know about the single digits? Explain
Solution:
To calculate probability, you need to understand your options. For
combination locks you would need to know the range of numbers and the number of numbers in
the combination and if zero is included in the choices.
If you want to see samples of the following change the Number
of NumbersandMaximum Number Generatedin the
generator included in Example 1.
