The document explains how to construct and use probability tree diagrams to calculate probabilities of independent events. It provides three examples: 1) Flipping two coins and calculating the probability of getting two heads. The tree diagram shows the possible outcomes at each branch and the probabilities are calculated by multiplying the probabilities along the branches. 2) Helen stopping at two sets of traffic lights and calculating the probability of stopping exactly once. The tree diagram assigns probabilities to stopping or not stopping at each light and branches to all outcomes. 3) Drawing sweets from a bag without replacement and calculating the probability of drawing one blue and one red sweet. The tree diagram again assigns probabilities at each branch and multiplies along the branches to calculate probabilities

1. Tree Diagrams
WALT complete a probability tree diagram for independent
events. Level 7
Starter
Draw a sample space diagram to show the possibilities
when you flip 2 coins.
What is P(2 Heads)?
Classwork
17/04/2020
Coin 1
Coin2
H T
H
T
HH HT
TH TT
𝟏
𝟒

2. I flip two coins, what is the probability that I get two heads?
Heads
Tails
Heads
Tails
Heads
Tails
1
2
1
2
1
2
1
2
1
2
1
2
P(HH) = x =1
2
1
2
1
4
P(HT) = x =1
2
1
2
1
4
P(TH) = x =1
2
1
2
1
4
P(TT) = x =1
2
1
2
1
4
Coin 1 Coin 2
Probabilities on
each branch add
up to 1 Possible outcomes are
shown on the end of the
branches
Multiply along the
branches to work out the
probabilities
P(HH) = 1
4

3. Helen passes through 2 sets of traffic lights on her way to work.
The probability that she stops at the first set is 0.3
The probability that she stops at the second set is 0.2
What is the probability that she has to stop exactly once?
Stops
Doesn’t
Stop
Stops
Doesn’t
Stop
Stops
Doesn’t
Stop
3
10
7
10
8
10
2
10
8
10
2
10 P(SS) =
3
10
x
2
10
= 6
100
P(SD) =
3
10
x
8
10
= 24
100
P(DS) =
7
10
x
2
10
=
14
100
P(DD) =
7
10
x
8
10
=
56
100
Lights 1 Lights 2
= 0.24 + 0.14
= 0.38

4. Red
Blue
Blue
Blue
Red
Red
7
10
6
9
3
9
3
10
2
9
7
9
I have a bag of sweets, 3 blue and 7 red. I pick one sweet out without
looking, eat it and then pick out and eat a second sweet. What is the
probability that I eat one blue and one red sweet?
Sweet 1 Sweet 2
P(RR) = x =7
10
6
9
42
90
P(RB) = x =7
10
3
9
21
90
P(BR) = x =3
10
7
9
21
90
P(BB) = x =3
10
2
9
6
90
42
90
7
15
=