PROBABILITY
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Probability tree diagrams
A tree diagram shows all the outcomes of two or more events.
You work out the probability of different outcomes by multiplying along the branches.
Probabilities on tree diagrams
The probability of Jamie being late for school on any day is 0.1
The tree diagram shows the probability of Jamie being late for school two days in a row.
You write the probability
of each event on
its branch
This branch shows Jamie
is late two days in a row
Monday
Multiply the probabilities
to give P(Late, Late)
Tuesday
Outcome
0.1
Late
Late, Late
0.1  0.1  0.01
0.9
Not late
Late, Not late
0.1  0.9  0.09
0.1
Late
Not late, Late
0.9  0.1  0.09
0.9
Not late
Not late, Late
0.9  0.9  0.81
Late
0.1
0.9
The probabilities on
each pair of branches
add up to 1
0.1  0.9  1
Not
late
P(Jamie is late two days in a row)  0.1  0.1  0.01
Marcus plays tennis. He either wins a
game or doesn’t win.
The probability that Marcus wins a
3
game is _​​ 4  ​​.
He plays two games of tennis.
(a) What is the probability Marcus
doesn’t win a game?
P(Doesn’t win) 
1  P(Wins)
​​ 14 ​​ 
 1  __
​​ 34 ​​  __
All the probabilities should add up to 1
0.01  0.09  0.09  0.81  1 ✓
1st game
Wins
​​ __34  ​​
​​  4 ​​
__
​​  14  ​​
__
3
Doesn’t
win
Outcome
Wins
Wins, Wins
Doesn’t win
3
Wins, Doesn’t win ​__
​ 34 ​​  __​ ​14 ​​  __
​ ​16
  ​​ 
Wins
3
Doesn’t win, Wins ​__
​ 14 ​​  __​ ​34 ​​  __
​ ​16
  ​​ 
Doesn’t win
Doesn’t win,
Doesn’t win
3
__
3
__
__
9
​​  4 ​​  ​ ​4 ​​  ​ ​16  ​​ 
__
1
​​ 4 ​​ 
_3
2nd game
​​ 4  ​​
__
1
​​ 4 ​​ 
(b) Complete this probability tree
diagram to show the probabilities
of all the possible outcomes.
(c) Work out the probability that Marcus wins both games.
1
__
1
__
__
1
​​  4 ​​  ​ ​4 ​​  ​ ​16  ​​ 
9
P(Wins, Wins)  __
​​ 34 ​​  __
​​ 43 ​​  __
​​ 16
  ​​ 
The probability that Peter passes a maths test is _​​ 2 ​​ 
3
The probability that Josie passes the test is ​​ _4 ​​ 
(a)What is the probability Peter does not
pass the test?
​ ​1 ​​
_ 
2
(b)What is the probability that Josie does
not pass the test?
(c) Complete this tree diagram.
……
(d)Work out the probability that both
Peter and Josie pass the maths test.
1
92
Peter
Josie
Outcome
Probability
_3
​​ 4 ​​ 
Pass
Pass, ……
_1
​​ 2 ​​  ……
Fail
Pass, ……
……
Pass
……, …… ……  ​_​ 34 ​​  5 ….
……
Fail
……, ……
 ….. 5 …..
Pass
…..  ….. 5 …..
Fail
…..  …..5 …..