Decision trees and dealing with uncertainty
Decision trees and dealing with uncertainty

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Decision trees and dealing with uncertainty

2 Check your understanding of probability

Allow approximately 30 minutes to complete this section.

In this section, you will attempt some questions and work through examples to test and embed your understanding of basic probability, as used in decision-making. First, try some simple questions on probability in Activity 2.

Activity 2 Probability quiz

Timing: Allow approximately 5 minutes to complete this activity

Select the response that best answers each question.

1. What does a probability of 1 mean?

a. 

This means that the event is certain to occur.


b. 

There is a 1 in 100 chance of the event occurring.


c. 

The event can only occur once.


d. 

There is a 1 in 10 chance of the event occurring.


The correct answer is a.

2. What must all the probabilities of all outcomes total to?

a. 

They must total to 1.


b. 

The total value of all outcomes.


c. 

0.50.


d. 

It depends on the event.


The correct answer is a.

Now study the following worked example in Box 1.

Box 1 Worked example on probability

What is the probability of throwing three heads and one tail, when throwing four coins at the same time?

To answer this, you need to explore the total number of possible outcomes. Here are two approaches to this problem.

Approach 1

Each coin will fall independently. The possible combinations are as follows. (Note that the scenarios of ‘three heads and one tail’ are in bold and italics below.)

HHHH

HHHT

HHTH

HHTT

HTHH

HTHT

HTTH

HTTT

THHH

THHT

THTH

THTT

TTHH

TTHT

TTTH

TTTT

From the list of possible combinations, you can conclude that there are 16 combinations, four of which (in italics) are three heads and one tail. This can be shown as:

multiline equation row 1 Probability of three heads and one tail equals four divided by 16 row 2 Blank equals 0.25

Approach 2

The number of combinations could also have been found as follows:

  • each coin has two possible outcomes

    If the first coin has two possible outcomes and the second also has two, then between them there are four combinations (i.e. 2 × 2 = 22 = 4)

  • adding a third coin (which has two outcomes) doubles the combinations (i.e. 2 × 2 × 2 = 23 = 8)

  • finally, the last coin makes it 16 (i.e. 24) as there are 4 coins, each of which may be heads or tails, then there are 4 combinations with 3 heads and one tail, so, the probability is: four divided by 16 equals 0.25.

In Activity 3, you will apply your understanding of probabilities in considering a different scenario.

Activity 3 Probability of ribbons in a box

Timing: Allow approximately 10 minutes to complete this activity

You place five ribbons in a box. They are coloured, black, blue, red, yellow and green. If you pull out two ribbons and the first is black, what is the probability that the second you select is blue?

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Answer

The probability of the second ribbon selection being blue is then:

one divided by four equals 0.25

You have now covered the basic ideas of probability and for the rest of this course you will learn how to apply these ideas in the context of making business decisions.

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