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COIN & DICE PROBABILITY: USING A TREE DIAGRAM

In this lesson we will look at some examples of probabilty problems involving coins, dice and spinners. We will use tree diagrams to help solve the problems. We will see that tree diagrams can be used to represent the set of all possible outcomes involving one or more experiments.

Example :

A coin and a die are thrown at random. Find the probability of:

a) getting a head and an even number

b) getting a head or tail and an odd number

Solution:

We can use a tree diagram to help list all the possible outcomes.

From the diagram, n(S) = 12

a) Let A denote the event of a head and an even number.

A = ((H, 2), (H, 4), (H, 6)} and n(A) = 3

b) Let B denote the event a head or tail and an odd number.

B = {(H, 1), (H, 3), (H, 5), (T, 1), (T, 3), (T, 5)}

Example:

Clare tossed a coin three times.

a) Draw a tree diagram to show all the possible outcomes.
b) Find the probability of getting:
(i) Three tails.
(ii) Exactly two heads.
(iii) At least two heads.

Solution:

a) A tree diagram of all possible outcomes.

b) The probability of getting:

(i) Three tails.

Let S be the sample space and A be the event of getting 3 tails.

n(S) = 8; n(A) = 1

P(A) =

ii) Exactly two heads.

Let B be the event of getting exactly 2 heads.

n(B) = 3

P(B) =

iii) At least two heads.

Let C be the event of getting at least two heads.

n(C) = 4

P(C) =

Example:

A spinner is labelled with three colours: Red, Green and Blue. Marcus spun the spinner once and tossed a coin once.

a) Draw a tree diagram to list all the possible outcomes.
b) Calculate the probability of getting blue on the spinner and head on the coin.
c) Calculate the probability of red or green on the spinner and tail on the coin.

Solution:

a) A tree diagram of all possible outcomes.