Download probability tree diagrams

PROBABILITY
TREE DIAGRAMS
Name: _______________________
Total Marks: ___________
Q.
1
2
3
4
5
6
7
8
9
10
11
www.justmaths.co.uk
Max Actual RAG
4
6
4
4
5
4
3
©JustMaths 2013
Q1. At the end of a training course candidates must take a test in order to
pass the course.
The probability of passing the test at the first attempt is 0.8
Those who fail will resit once.
The probability of passing the resit is 0.5 and no further attempts are
allowed.
a) Complete the tree diagram, which shows all possible outcomes.
(1 Mark)
b) What is the probability that a candidate fails both attempts and so fails
the course?
(2 Marks)
c) What is the probability that a candidate passes the course?
(1 Mark)
www.justmaths.co.uk
©JustMaths 2013
Q2. A bag contains 5 green and 3 red balls. A ball is taken from the bag at
random and replaced. Another ball is then taken from the bag at
random.
Complete the tree diagram.
(1 Mark)
b)
What is the probability that both balls are red?
(2 Marks)
c)
Some more green balls are added to the 5 green and 3 balls in the bag.
A ball is taken from the bag at random and replaced. Another ball is
then taken from the bag at random.
The probability that both balls are red is now
How many green balls were added to the bag?
(3 Marks)
www.justmaths.co.uk
©JustMaths 2013
Q3. A bag contains 6 blue ad 4 white balls. A ball is taken at random and
replaced. Another ball is then taken from the bag at random.
(1 Mark)
a) Complete the tree diagram.
b) What is the probability that both balls are the same colour?
(3 Marks)
www.justmaths.co.uk
©JustMaths 2013
Q4. These ten letters are placed in a hat:
S
T
A
T
I
S
T
I
C
S
A letter is drawn from the hat at random, noted and replaced. Another
letter is drawn from the hat at random and noted.
a) Complete the tree diagram to show whether or not the letters drawn
are vowels (A or I) or consonants (C, S or T).
(1 Mark)
b) Work out the probability that at least one of the letters drawn is a
vowel.
(3 Marks)
www.justmaths.co.uk
©JustMaths 2013
Q5. Two ordinary six-sided dice are used in a game. One dice is fair and the
other is biased.
The probability of throwing a six with the biased dice is p.
The two dice are thrown.
The probability of getting exactly one six is
Using the tree diagram or otherwise, work out p.
(5 Marks)
www.justmaths.co.uk
©JustMaths 2013
Q6. In a game of chess, a player can win, draw or lose. The probability that
Vishi wins any game of chess is 0.5
The probability that Vishi draws any game of chess is 0.3
Vishi plays 2 games of chess.
a) Complete the probability tree diagram.
(2 Marks)
b) Work out the probability that Vishi will win both games.
(2 Marks)
www.justmaths.co.uk
©JustMaths 2013
Q7. Two fair coins are thrown. Ahmed says “the probability of obtaining two tails is less than 0.5”. Is Ahmed correct? You must show all the necessary working to justify
your answer.
(3 Marks)
www.justmaths.co.uk
©JustMaths 2013