Tree Diagrams Grade B 20 Apr 2023
LO: Draw and use a tree diagram to find conditional probabilities.
LO: Draw and use a tree diagram to find conditional probabilities.
Z
Z
Scissors Paper Stone
Scissors beats paper (cuts it)
Paper beats stone (wraps it)
Stone beats scissors (blunts it)
Showing the same is a draw
Create the following table to complete as you play
Play the game 30 times Add up your tally for the Total Fill in the 3 probabilities (these are
the Total / 30) Use the calculator these into
convert these into decimals Enter your results into the class
spreadsheet
Result Tally Total Probability
A Wins
B Wins
Draw
Is it a fair game?
Scissors Paper Stone
Can you find a way to calculate the probabilities of the game using a tree diagram?
Player A
Scissors
Paper
1/3
1/3
Stone
1/3
Z
Scissors Paper Stone
Player A
Scissors
Paper
1/3
1/3
Stone
1/3
Scissors
Paper
Stone
1/3
1/31/3
Scissors
Paper
Stone
1/3
1/31/3
Scissors
Paper
Stone
1/3
1/31/3
Player B
Draw
A Wins
B Wins
B Wins
Draw
A Wins
A Wins
B Wins
Draw
1/9
1/9
1/9
1/9
1/9
1/9
1/9
1/9
1/9
9/9
P(A Wins) = 1/9 + 1/9 + 1/9
= 3/9 = 1/3
P(B Wins) = 1/9 + 1/9 + 1/9
= 3/9 = 1/3
P(Draw) = 1/3
AND
1/3 x 1/3 =
1/3 x 1/3 =
1/3 x 1/3 =
1/3 x 1/3 =
1/3 x 1/3 =
1/3 x 1/3 =
1/3 x 1/3 =
1/3 x 1/3 =
1/3 x 1/3 =
OR
AND: xOR: +
Z
Two Dice
First dice Second dice
Six
Six
SixNot six
Not six
Not six
PROBABILITIES
First dice Second dice
Six
Six
Six
Not six
Not Six
Not six
6
1
6
5
6
1
6
5
6
1
6
5
PROBABILITIES
36
1
6
1
6
1
36
5
6
5
6
1
36
5
6
1
6
5
36
25
6
5
6
5
First dice Second dice
Six
Six
Six
Not six
Not Six
Not six
6
1
6
5
6
1
6
5
6
1
6
5
The probability that Colin is late for work, on any given day = 0.2
First day Second day
Late
Late
Late
Not late
Not late
Not late
First day Second day
Late
Late
Late
Not late
Not late
PROBABILITIES
0.2
0.2
0.2
0.8
0.8
0.8
Not late
First day Second day
PROBABILITIES
Late
Not late
0.2
0.8
Late
Late
Not late
0.2
0.2
0.8
0.8
Not late
0.2 x 0.2 = 0.04
0.8 x 0.8 = 0.64
0.8 x 0.2 = 0.16
0.2 x 0.8 = 0.16
Make up a story of your own
Draw a tree diagram
Label all possible outcomes
AQA
Page 176
Ex 5G
Colin has a tin of sweets:
6 chocolates and 4 mintsProduce a tree diagram to show the probabilities of taking one sweet followed by another sweet.
What is the probability of taking two of the same type?
First sweet Second sweet
Chocolate
Mint
Chocolate
Chocolate
Mint
Mint
PROBABILITIES
First sweet Second sweet
C
CM
M
M
10
6
10
4
9
5
9
4
9
6
9
3
90
30
9
5
10
6
C90
24
9
4
10
6
90
24
9
6
10
4
90
12
9
3
10
4
What is the probability of taking two of the same type?
Chocolate and chocolate =
Mint and mint =
90
30
9
5
10
6
90
12
9
3
10
4
So two of the same = 90
42
90
12
90
30
Complete the worksheet for Thursday’s lesson.
Recommended
