Tree Diagrams Grade B 3-Nov-14

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.