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  • GETSenPhaseMaths display tagshide tags

    This module is included inLens: Siyavula: Mathematics (Gr. 7-9)
    By: Siyavula

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Probability

Module by: Siyavula Uploaders. E-mail the author

MATHEMATICS

More Geometry, Data Handling and Probability

EDUCATOR SECTION

Memorandum

20.3 (a) (i) a half (one out of 2)

(ii) a half (one out of 2)

(c) one quarter (one out of 6)

(d) 2 out of 21

20.4 (a) one sixth (one out of six)

20.5 six out of 36 (one sixth)

22. ALL THE MATHS IS DONE!

MODULE TEST 9

1. Check learner’s effort.

2. glide

3. (a) Only a part of the group was questioned to get information

.

(b) About the possibility that something might happen.

4. (a) 10

(b) 10

(c) 10,6

5. (a) picture graph / pictogram

(b) Learners are six years and older in grade 1. / Nobody is younger than six years.

(c) 110

(d) 30

(e) 680

6.

7.4 4 out of 32 (one eigth).

LEARNERS SECTION

Content

ACTIVITY: Probability [LO 5.10, LO 5.9]

20. PROBABILITY

20.1 Class discussion

a) What chance do you have of passing Grade 7?

b) What is the chance that it will rain today?

c) What chance does your team (any sport) have of winning the next match?

d) What is your chance of winning the Lotto?

e) What is the chance that one day you will walk on the moon?

20.2.1 Did you know?

In the above cases, you have actually estimated the possibility that something will or will not happen.

20.2.2 Did you also know?

Probability stretches from “no chance” that something will happen to “it will definitely happen”.

A probability of 0 means that the happening will never occur.

A probability of 1 means that the happening will definitely occur.

20.2.3 IMPORTANT to KNOW:

The probability that something will happen depends on:

The number of times it can happen

Total number of possibilities

The closer you answer is to 1, the more likely it is

that the event/happening will take place.

20.3 Work with a friend and answer the following questions:

a) You throw a coin up into the air. What is the probability that it will fall:

i) heads up? ________________________

ii) tails up? _________________________

b) Throw a coin into the air 50 times. Your friend can help you keep record which side of the coin faced upwards each time it landed.

i) Complete the table:

Table 1
 
 
Heads Tails
Probability
Heads Tails
E.g. 4 6 4 10 4 10 size 12{ { { size 8{4} } over { size 8{"10"} } } } {} 6 10 6 10 size 12{ { { size 8{6} } over { size 8{"10"} } } } {}
First 10 throws: ............. ............. ............. .............
Second 10 throws: ............. ............. ............. .............
Third 10 throws: ............. ............. ............. .............
Fourth 10 throws: ............. ............. ............. .............
Fifth 10 throws: ............. ............. ............. .............

ii) What is the average for your throws for:

a) heads: _______________________

a) tails: ________________________

c) What is the probability that both coins will land heads up if you throw them up at the same time?

_____________________________________________________________________

d) A person participating in the Lotto game must take a blue ball out of the container in order to win a prize. If there are 19 pink balls and 2 blue balls in the container, what is the probability that the contestant will win a prize?

_____________________________________________________________________

20.4 Work on your own. You will need a di.

a) What is the probability that the 3 will fall on top when you throw the dice? _____________________________________________________________________

b) Now throw the di 15 times. In the space below make a tick (√) every time the 3 lands on top.

Now write the total number of ticks as a fraction where the denominator is 15. _____________________________________________________________________

Is your answer close to one sixth (use your calculator) _________________________

Can you explain this? __________________________________________________

_____________________________________________________________________

20.5 Did you know?

It would be pure chance if you achieved a probability of one sixth in the above activity. Practical probability is based on what you actually did. Theoretical probability is only an attempt to predict what might happen.

The more times that you throw the di, the closer the practical

and theoretical probabilities should come to each other.

20.6 BRAINTEASER

  • What is the probability that you will get 7, if you throw two dice at the same time and add the numbers that are showing upwards?

_____________________________________________________________________

_____________________________________________________________________

21. Time for self-assessment

Table 2
  • Colour in the face that is true of you:
      
I can explain the concept “probability”. graphics1.png graphics2.png graphics3.png
I know what a probability of 0 means. graphics4.png graphics5.png graphics6.png
know what a probability of 1 means. graphics7.png graphics8.png graphics9.png
I know the “formula” to determine probability. graphics10.png graphics11.png graphics12.png
I was able to correctly calculate the probability in the given questions. graphics13.png graphics14.png graphics15.png

22. For FUN!

  • Use the given co-ordinates and decode the code:

(9,9) (9,2) (1,10) (1,10) (3,2) (1,0) (6,10) (2,6)

............................................ .........................

(4,1) (3,2) (1,10) (1,10) (5,8) (8,5) (6,10) (1,2) (6,10)

............................................ ......................................

(8,5) (6,10) (1,2) (1,8) (8,5) (9,9) (3,8) (9,1) (5,8) (6,10)!!

................. ......................................................................!!

Figure 1
Figure 1 (graphics16.png)

Assessment

Learning Outcome 5:The learner will be able to collect, summarise, display and critically analyse data in order to draw conclusions and make predictions, and to interpret and determine chance variation.

Assessment Standard 5.9:We know this when the learner critically reads and interprets data presented in a variety of ways to draw conclusions and make predictions sensitive.

Assessment Standard 5.10:We know this when the learner performs simple experiments where the possible outcomes are equally likely.

MODULE TEST

1. Reduce the frog on a scale 2:1.

Figure 2
Figure 2 (graphics17.png)

(3)

2. What kind of transformation was in the following figure?

Figure 3
Figure 3 (graphics18.png)

_____________________________________________

(1)

3. Explain the following concepts:

a) random test: ____________________________________________________

_____________________________________________________________________

_____________________________________________________________________

(2)

b) probability: _____________________________________________________

_____________________________________________________________________

_____________________________________________________________________

(2)

4. Look at the following:

A group of learners’ marks out of 15 were as follows:

6; 11 ; 12 ; 15 ; 9 ; 10 ; 10 ; 10 ; 8 ; 15

a) Calculate the mode:_______________________________________________

_____________________________________________________________________

_____________________________________________________________________

(2)

b) Calculate the median: _____________________________________________

_____________________________________________________________________

_____________________________________________________________________

(2)

c) Calculate the arithmetic mean (average): ______________________________

_____________________________________________________________________

_____________________________________________________________________

(2)

5. Study the graph and answer the following questions:

Figure 4
Figure 4 (graphics19.png)

a) What is this type of graph called?

_____________________________________________________________________

(1)

b) Why does it “jump” from 0 to 6?

_____________________________________________________________________

_____________________________________________________________________

(1)

c) How many learners are 7 years old?

_____________________________________________________________________

(1)

d) How many more 9 year old learners are there than 12 year olds?

_____________________________________________________________________

(1)

e) How many learners are there in the school?

_____________________________________________________________________

(1)

6. Represent the information given in question on a line graph.

(3)

7. What is the probability that you will take a black ball from a container containing 12 red, 6 green, 4 black, 2 yellow and 8 blue balls?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

(2)

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