21 lo4 probability

8/4/2019 21 LO4 Probability

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Grade 12 Mathematical Literacy

LO4 Probability: Two-way tables and tree diagrams

1. Two six-sided dice are thrown at the same time.

1.1 Consider the possible outcomes and copy and complete thetable below.

Scores on two dice thrown at thesame time

S c o r

e s

o n

f i r s t

d i c e

6 6;1

5 5;1

4 4;1

3 3;1

2 2;11 1;1

1 2 3 4 5 6

Score on second dice

1.2 How many possible outcomes are there?

1.3 What is the probability of rolling the samescore on both dice?

1.4 What is the probability of rolling a combinationthat includes the score 3?

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http://images.google.co.za/imgres?imgurl=http://wilderdom.com/images/dice.gif&imgrefurl=http://wilderdom.com/games/descriptions/Dice.html&h=413&w=552&sz=7&hl=en&start=1&tbnid=uH9WngYizCMl4M:&tbnh=100&tbnw=133&prev=/images%3Fq%3Ddice%26gbv%3D2%26svnum%3D10%26hl%3Den%26sa%3DG




2. The table below shows the result of the Durban July horse raceand the odds of each horse at the start of the race.

Position in race Name of horse Odds Probability1 Wolfpower 14 to 1070

14

1,or

2 Pocket Rocket 9 to 1

3 Gatecrasher 20 to 3

4 Seacottage 33 to 1

5 Seabiscuit 15 to 2

6 Oceanspirit …. to 1040

25

1,or

7 Sea Mist …. to 50890

56

5,or

8 Braveheart 11 to 8

9 Big Charles 150 to 1

10 Catseyes 200 to 1

2.1 Copy and complete the table.

2.2 Which horse was the favourite?

2.3 Did the horses finish in the order as reflected by their odds?

2.4 What important lesson can you learn from your findings in 2.3above?





3. A survey was conducted about a particular breakfast cereal. 200 males and 160females were interviewed. The tablebelow shows some of the results:

MALES FEMALES TOTALS

Liked the cereal (a) 35 155

Did not like the cereal 80 (b) (c)

TOTAL 200 160 (d)

3.1 Copy and complete the table by calculating the values of theletters (a, b, c and d) in the table.

3.2 What is the probability of a female liking the cereal?

3.3 What is the probability of a male disliking the cereal?

4. Xoli plans to spend a weekend with his friends. He is undecidedabout what clothes to take with him. He has to choose from thefollowing items:

Two pairs of trousers: blue jeans or black trousers.Three shirts: a blue T-shirt, a green T-shirt or a white shirt.Two pairs of shoes: a black pair or a grey pair.

4.1 Draw a tree diagram to show all the possible combinations of trousers, shirts and shoes.

4.2 If each pair of trousers, each shirt and each pair of shoes havean equal chance of being chosen, what is

the probability that Xoli will wear his blue

jeans with his black shoes?

4.3 What is the probability of Xoli wearing hisblack trousers with a red shirt?





5. Jarryd has seven blue socks and five red socks in his drawer.One dark winter’s morning he gets dressed for school withoutturning on the light. He chooses two socks from his drawer.

Make use of a tree diagram to determine the probability of himchoosing a matching pair.





ANSWERS

1.1

Scores on two dice thrown at the same time

S c o r e s o n

f i r s t

d i c e

6 6;1 6;2 6;3 6;4 6;5 6;65 5;1 5;2 5;3 5;4 5;5 5;6

4 4;1 4;2 4;3 4;4 4;5 4;6

3 3;1 3;2 3;3 3;4 3;5 3;6

2 2;1 2;2 2;3 2;4 2;5 2;6

1 1;1 1;2 1;3 1;4 1;5 1;6

1 2 3 4 5 6

Score on second dice

1.2 6 x 6 = 36 possible outcomes

1.3 1706

1

36

6,==

1.4 31036

11,=





2.1

Position in race Name of horse Odds Probability

1 Wolfpower 14 to 1070

14

1,or

2 Pocket Rocket 9 to 1110

9

1,

or

3 Gatecrasher 20 to 3150

20

3,or

4 Seacottage 33 to 1030

33

1,or

5 Seabiscuit 15 to 2130

15

2,or

6 Oceanspirit …. to 1040

25

1,or

7 Sea Mist …. to 50890

56

5,or

8 Braveheart 11 to 872720

11

8,or

9 Big Charles 150 to 1006660

150

1,or

10 Catseyes 200 to 10050

200

1,or

2.2 With a probability of 0,7272, Braveheart was the favourite.

2.3 No. Braveheart came 8th. Four other horses were expected to

do better than Wolfpower, who came first.

2.4 Although ‘odds’/probability of winning isgiven, there is not guarantee when gambling.The probability of losing your money whengambling appears quite high if the abovescenario is an indication of what happensgenerally in gambling.

3.1MALES

FEMALES TOTAL

Liked the cereal 120 35 155

Did not like the cereal 80 125 205

TOTAL 200 160 360





3.2 218032

7

160

35,==

3.3 405

2

200

80,==

4.1 Tree Diagram:

4.2 0833012

1,=

4.3 0 probability, as there is no red shirt.5.


http://images.google.co.za/imgres?imgurl=http://www1.istockphoto.com/file_thumbview_approve/1999635/2/istockphoto_1999635_the_clothes_you_wear.jpg&imgrefurl=http://www.istockphoto.com/file_closeup/%3Fid%3D1999635%26refnum%3D425251&h=368&w=380&sz=43&hl=en&start=25&tbnid=b3J0ZEriGNBINM:&tbnh=119&tbnw=123&prev=/images%3Fq%3Dclothing%2Bmodel%26start%3D18%26gbv%3D2%26ndsp%3D18%26svnum%3D10%26hl%3Den%26sa%3DN




The probability of choosing two blue socks:

P(BB) =132

42

11

6

12

7=×

The probability of choosing two red socks:

P(RR) =132

20

11

4

12

5=×

As both blue and red socks can result in a matching pair we have toadd the two probabilities together:

P(Matching Pair) = P(BB) + P(RR)

= 4696066

31

132

62

132

20

132

42,===+


21 lo4 probability

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