In these lessons we will look at some examples of probability 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 dice 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: *

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) 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: *

b) The probability of getting blue on the spinner and head on the coin.

Let

n(

P(

c) The probability of red or green on the spinner and tail on the coin.

Let

n(*B*) = 2

P(*A*) =

Problem: A coin is biased so that it has 60% chance of landing on heads. If it is thrown three times, find the probability of getting:

(a) 3 heads,

(b) 2 heads and a tail,

(c) at least one head. The following video gives more examples of probability involving coins and using tree diagrams. You flip 3 coins. What is the theoretical probability of getting 2 heads and 1 tails?

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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