ProbabilityGrade 8

Probability is all about calculating, estimating or predicting what might happen in the future.

Let’s start off by discussing some important probability language.

We will use two coins in our discussion.

Eksperiment: Hierdie eksperiment behels die opskiet van

een muntstuk, gevolg deur die opskiet van ’n tweede

muntstuk.

Each tossing of the one coin followed by the other is called a trial.

Outcome: An outcome is the result of a trial. When one coin is tossed followed by the

tossing of the other coin, there are four possible outcomes:Eerste muntstuk

‘n kop is (K) en die tweede muntstuk ‘n kop is (K)

• First coin is a head (H) and the second coin is a head (H)

• First coin is a head (H) and the second coin is a tail (T)

• First coin is a tail (T) and the second coin is a head (H)

• First coin is a tail (T) and the second coin is a tail (T)

Experiment:

Trial:

The experiment here involves the tossing of the

one coin followed by the tossing of the other.

Steekproefruimte:Sample space: Die versameling van alle moontlike uitkomste word genoem die

Event:

An event is a collection of one or more outcomes of an experiment.

Probability:

The set of all possible outcomes is called the sample space.

We write this as follows: S = {HH, HT, TH, TT}

There are a total of four possible outcomes in the sample space.

Event head with first throw HH, HT

The number of outcomes in event A is 2.

Event B Getting at least one tail per trail

HT, TH, TT

The number of outcomes in event B is 3.

Probability of an event happening is the number of outcomes in an event

divided by the total number of outcomes in the sample space.

Sample space:

Sample space:

The scale of probability

Example 1

A bag contains three bar ones, four crunchies and seven kit kats. One chocolate is taken out

of the bag at random. What is the probability of choosing::

(a) A Bar One?

There are a total of 14 chocolates in the bag of which there are 3 bar ones.

P (Bar one) =3

14

(b) A Crunchie?

There are a total of 14 chocolates in the bag of which there are 4 crunchies.

P(Crunchies )=4

14

=2

7

Example 2

A six-sided die is thrown. Determine the probability of rolling:

(a) the number 5

There are six numbers (outcomes) in the sample space S = {1, 2, 3, 4, 5, 6}

P(5) = 1

6

(b) an even number

The event is choosing the outcomes{ 2, 4, 6}.

P(even number) = 3

6= 1

2

(c) a natural number

The event is choosing the outcomes {1, 2, 3, 4, 5, 6}.

P(natural number) = 6

6= 1

(d) a natural number greater than 6

The event is choosing the outcomes {7, 8, 9, ........} A six-sided die doesn’t have

any of these numbers.

P(natural number > than 6) =0

6= 0

Example 3

There are 52 cards in a pack excluding the joker.

Determine the probability of drawing, at random:

(a) a queen.

There are four queens.

P(queen) =4

52=

1

13

(b) a queen of hearts.

There is one queen of hearts.

P(Queen of hearts) =1

52

(c) a spade or a club.

There are 13 spades and 13 clubs.

P(spade or club) =13

52+

13

52

=26

52=

1

2

Example 4

A die is rolled 300 times. Predict how many times you would expect to roll a number

greater

than 4.

The numbers greater than 4 are {5,6} .

P(number greater than 4) =2

6=

1

3

Predicted number of times = 1

3× 300

= 100

1. One card is drawn from a pack of playing cards that consists of 52

cards. What is the probability that the type of card is:

1.1.1 A king?

1.1.2 A diamond?

1.1.3 A queen of hearts?

1.1.4 A black king?

1.1.5 Not a heart?

Worksheet (Do the following in your book)

1.2 What is the probability that:

1.2.1 the sun will rise in the east?

1.2.2 a triangle has three sides?

1.2.3 a newborn baby will be a boy?

1.2.4 this month has 32 days?

1.2.5 it will snow in February in South- Africa?

1.2.6 a dice will land on an even number?

1.3 A bag contains five red balls, four green balls and seven white balls. Calculate theprobability of selecting, at random:

1.3.1 a red ball

1.3.2 a green ball

1.3.3 a white ball

1.3.4 a blue ball

1.3.5 any ball

1.3.6 a red or white ball

1.3.7 a ball that is not red

1.4 A letter is chosen at random from the word PROBABILITY. Determine theprobability of choosing:

1.4.1 the letter A

1.4.2 the letter W

1.4.3 the letter L

1.4.4 the letter I

1.4.5 a vowel

1.4.6 die letter C

1.4.7 die letter A of I

1.5 A die is rolled 600 times. Predict how many times you would expect to roll the

number 5.

1.6 A die is rolled 3500 times. Predict how many times you would expect to roll an odd

number.

1.7 The spinner shown has equal numbered segments.

1.7.1 What is the probability of obtaining the number 4 on the first spin?

1.7.2 What is the probability of obtaining a factor of 4 on the second spin?

1.7.3 How many 3’s would you expect in 1 800 spins?

1.7.4 What is the probability of obtaining the number 3 in 600 spins?

A bag contains 3 green discs and 4 white discs. One ball is drawn at random and then replaced. A second ball is then

drawn. Complete the given tree diagram and answer the following questions.

TREE DIAGRAMS

First draw

𝑛 𝑔𝑟 =3

7

𝑛 𝑤 =4

7

𝑛 𝑔𝑟 =3

7

𝑛 𝑤 =4

7

Second

draw

1. Find the probability that

1.1 both balls are green

𝑃 𝐺 𝑎𝑛𝑑 𝐺 =3

7×3

7

=9

49

1.2 both balls are white

𝑃 𝑊 𝑎𝑛𝑑 𝑊 =4

7×4

7

=16

49

1.3 the first ball is green and the second ball is white

𝑃 𝑔𝑟𝑒𝑒𝑛 𝑎𝑛𝑑 𝑡ℎ𝑒𝑛 𝑤ℎ𝑖𝑡𝑒 =3

7×4

7

=12

49

A grade 8 class undertakes an educational tour to Cape Town. One morning they are given the opportunity to make a

choice between the following two activities:

A: A visit to Robben Island.

B: Going to Table Mountain.

The learners visiting Robben Island have a further choice between a tour with a bus or a tour where one could walk to

the different sights of interest.

The learners going to Table Mountain have the choice of either climbing Table Mountain or going up by cable car.

There are 40 learners in the grade 8 class. Eighteen learners decide to go to Robben Island, six of them decide do the

walking tour. Sixteen of the learners decide to climb Table Mountain.

1. Draw a tree diagram to represent the above information.

2. Make use of a tree diagram to answer the following questions:

Suppose one learner gets injured. What is the probability that

2.1 the learner is on Robben Island?

2.2 the learner is busy climbing Table Mountain?

2.3 the learner is on Robben Island on the bus tour?