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For Teachers
Introduction Taking a Chance – Probability Gems provides students with a step by step approach to seven fundamental areas of probability: basic probability, complementary events, two way tables, venn diagrams, tree diagrams, independent events and dependent events. With the help of Sonny the magician, students are taken step by step through worked examples in the program. Each chapter is followed by a selection of questions for students to complete.
Timeline 00:00:00 Probability basics 00:04:51 Complementary events 00:10:53 Venn diagrams 00:13:58 Tree diagrams 00:17:20 Independent events 00:19:40 Dependent events 00:22:47 Credits 00:23:18 End program
Related Titles Solving Linear Equations Algebra: The Basics Statistics – Sampling, Surveying and Data Analysis Interest, Loans and Credit
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Student Worksheet
Initiate Prior Learning 1. State whether these events are likely to occur (high probability) or unlikely to occur (low
probability):
a) Winning a raffle if you have 10 tickets out of 1000 _________________________________________________________________________________
b) Raining if there are lots of black clouds in the sky. _________________________________________________________________________________
c) Catching a fish on a hook without bait. _________________________________________________________________________________
d) Scoring 100% on a very hard test. _________________________________________________________________________________
e) Doing your homework _________________________________________________________________________________
f) Think of another 2 high probability and 2 low probability examples, share these with a friend. _________________________________________________________________________________ 2. In groups of 2-3, use a newspaper and look for as many examples of probability as you can find.
Some of the obvious ideas will be lotto results and the sporting section. Make a collage of your findings.
3. Find out how probability is used in lotto. Would you buy a ticket? 4. Research Blaise Pascal and how he developed the theory of probability. What is Pascal’s triangle?
What were some of the gambling problems he worked out the odds for?
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Active Viewing Guide Probability basics 1. A pack of cards contains 52 playing cards. Calculate the following probabilities.
a) Pr (8 of hearts)
b) Pr (red 8)
c) Pr (any colored 8)
d) Pr (picture card)
e) Pr ( numbered card 2-10) 2. A box of teddy bears contains 3 polar bears, 1 koala bear, 2 black bears and 4 panda bears. If one
bear is selected at random, calculate the probability that:
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3. If one letter is selected from the word ELEPHANT, what is the probability it will be an E? 4. Seven cards are numbered from 1 – 7. If one card is drawn at random, what is the probability that
it is an odd number? Complementary Events 1. If the probability of rolling an even number on a dice is 3/6, what is the probability of not rolling an
even number? 2. If the probability of choosing a queen in a pack of cards is 4/52, what is its complement? 3. Using a dice, roll it 10 times and record your results. Using your results calculate:
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4. On a shelf there are 7 math, 2 history, 3 art and 4 science books. What is the probability of not
choosing a math book? Two way tables 1. Complete the following table:
Swimming Gym Total
Boys 25
45
Girls
Total 64
100
2. Complete the following table and then answer the questions about types of coffee bought.
Coffee is sold in three types and in three weights.
a) How many people bought 100g of powdered coffee?
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c) Out of the packets weighing 200g, what is the probability the packet bought contained
granules? Venn diagrams 1. Twenty golf balls are labeled from 1 to 20 and placed in a bag. One ball is drawn at random to
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2. A class of 27 students are asked if they like science, math and English. They provided the
following results:
• 3 students liked all three subjects
• 3 students liked both science and math
• 2 students liked both English and math
• 6 liked English only
• 4 liked math only
• 7 liked science only
• 2 do not like any of the subjects
a) Draw a venn diagram for this information.
b) Find the probability of randomly selecting a student who:
You may download and print one copy of these support notes from our website for your reference. Further copying or printing must be reported to CAL as per the Copyright Act 1968.
You may download and print one copy of these support notes from our website for your reference. Further copying or printing must be reported to CAL as per the Copyright Act 1968.
Tree Diagrams 1. Draw a tree diagram for the tossing of a coin twice.
a) List all the possible outcomes. Eg. HH
b) Calculate the probability of each outcome (in a decimal value). Add all the probabilities to find the total. Explain your answer.
c) Calculate the following probabilities:
i. Pr (TT)
ii. Pr (one head and one tail)
iii. Pr (at least one head)
iv. Pr (no heads) 2. A bag contains 1 red, 1 blue and 1 white marble. A marble is drawn from the bag, the color noted,
replaced and another marble is drawn.
a) Draw a tree diagram to represent the possible outcomes.
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b) Calculate:
i. Pr(WW)
ii. Pr (not WW)
iii. Pr (at least one red)
iv. Pr (one red and one blue) 3. Heath and Jessica decide to play a game. In the first round Heath has a 0.65 chance of winning.
In the second round he doesn’t think as clearly and his chance of winning is 0.30.
a) Draw a tree diagram to represent two games played by Heath and Jessica.
b) List all the possible outcomes and their probability.
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Independent Events 1. A pack of playing cards contains 26 red cards. As cards were selected, the result was recorded
and the card replaced. Calculate the following probabilities:
a) Pr (2 kings)
b) Pr (2 cards chosen are not picture cards)
c) Pr (first card is a picture card and the second is an even number) 2. A box contains 9 balls: 4 red, 2 blue, 3 green. If three balls are drawn one at a time and replaced,
calculate the following probabilities:
a) 3 green balls are chosen
b) the only red ball chosen is last
c) the first ball is blue, the second ball is green and the third ball is red Dependent Events 1. A ‘lucky dip’ at a school fete contains 20 prizes, all of the same size. If 5 prizes are a set of
crayons, find the probability that, from the first 4 children to sample the dip:
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c) 4 children receive crayons
2. A box contains 9 balls, 4 red, 2 blue, 3 green. If three balls are drawn one at a time without
replacement, calculate the following probabilities:
a) 3 green balls are chosen
b) the only red ball chosen is last
c) the first ball is blue, the second ball is green and the third ball is red
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Extension Activities 1. Design a “how to” poster or Power Point presentation for one of the chapters in the program to
teach other students the technique. 2. Complete a class survey on a topic of your choice, such as football teams. Put this data into a
table and write five questions that another student will answer based on probability. Correct their work.
3. Using the internet investigate the ‘Birthday Paradox”. Can you calculate the probability that 2
students in your class have their birthday on the same day?
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Suggested Student Responses
Initiate Prior Learning 1. State whether these events are likely to occur (high probability) or unlikely to occur (low
probability):
a) Winning a raffle if you have 10 tickets out of 1000 Low
b) Raining if there are lots of black clouds in the sky. High
c) Catching a fish on a hook without bait.
Low
d) Scoring 100% on a very hard test. Low (answer will vary depending on students)
e) Doing your homework
Vary!
f) Think of another 2 high probability and 2 low probability examples, share these with a friend. Own examples
2. In groups of 2-3, use a newspaper and look for as many examples of probability as you can find.
Some of the obvious ideas will be lotto results and the sporting section. Make a collage of your findings. Poster
3. Find out how probability is used in lotto. Would you buy a ticket?
Research 4. Research Blaise Pascal and how he developed the theory of probability. What is Pascal’s triangle?
What were some of the gambling problems he worked out the odds for? Research
You may download and print one copy of these support notes from our website for your reference. Further copying or printing must be reported to CAL as per the Copyright Act 1968.
Active Viewing Guide Probability basics 1. A pack of cards contains 52 playing cards. Calculate the following probabilities.
a) Pr (8 of hearts) 1/52 = 0.02
b) Pr (red 8)
2/52 = 0.038
c) Pr (any colored 8) 4/52 = 0.08
d) Pr (picture card)
12/52 = 0.23
e) Pr ( numbered card 2-10) 36/52 = 0.69
2. A box of teddy bears contains 3 polar bears, 1 koala bear, 2 black bears and 4 panda bears. If one
bear is selected at random, calculate the probability that:
a) Pr (polar) 3/10 = 0.3
b) Pr (koala)
1/10 = 0.1
c) Pr (koala or a panda) 5/10 = 0.50
d) Pr (polar or koala or black)
6/10 = 0.60 3. If one letter is selected from the word ELEPHANT, what is the probability it will be an E?
2/8 = 0.25 4. Seven cards are numbered from 1 – 7. If one card is drawn at random, what is the probability that
it is an odd number? 4/7 = 0.57
Complementary Events 1. If the probability of rolling an even number on a dice is 3/6, what is the probability of not rolling an
even number? 3/6 = 0.50
2. If the probability of choosing a queen in a pack of cards is 4/52, what is its complement?
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3. Using a dice, roll it 10 times and record your results. Using your results calculate:
Results will vary dependent on student outcomes of completing the rolling of dice. Class discussion is required to see if results are similar.
a) Pr (rolling a 4)
b) Pr (not rolling a 4)
c) Pr ( rolling a number 4 and above)
d) Pr ( rolling a number less than 4)
4. On a shelf there are 7 math, 2 history, 3 art and 4 science books. What is the probability of not
choosing a math book? 9/16 = 0.56
Two way tables 1. Complete the following table:
Swimming Gym Total
Boys 25 20 45
Girls 39 16 55
Total 64 36 100
2. Complete the following table and then answer the questions about types of coffee bought.
Coffee is sold in three types and in three weights.
a) How many people bought 100g of powdered coffee?
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b) How many people bought ground coffee?
120
c) Out of the packets weighing 200g, what is the probability the packet bought contained granules? 45/130
Venn diagrams 1. Twenty golf balls are labeled from 1 to 20 and placed in a bag. One ball is drawn at random to
check the following events:
• Event A: a number less than 10
• Event B: a multiple of 4
• Event C: even number
a) List the events A, B, C Event A: 1 – 10 Event B = 4, 8, 12, 16, 20 Event C: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
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2. A class of 27 students are asked if they like science, math and English. They provided the
following results:
• 3 students liked all three subjects
• 3 students liked both science and math
• 2 students liked both English and math
• 6 liked English only
• 4 liked math only
• 7 liked science only
• 2 do not like any of the subjects
a) Draw a venn diagram for this information.
b) Find the probability of randomly selecting a student who:
i. Likes math only 4/27 = 0.15
ii. Likes all three subjects
3/27 = 0.11
iii. Does not like science 14/27 = 0.52
iv. Likes math or science but not English
14/27 = 0.52
v. Does not like any of the subjects 2/27 = 0.074
vi. Likes at least one of the three subjects
25/27 = 0.93 Tree Diagrams 1. Draw a tree diagram for the tossing of a coin twice.
a) List all the possible outcomes. Eg. HH HH, HT, TH, TT
b) Calculate the probability of each outcome (in a decimal value). Add all the probabilities to
find the total explain your answer. HH = 0.25, HT = 0.50, TT = 0.25, All add up to 1, all probability is between 0-1.
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ii. Pr (one head and one tail) 0.50
iii. Pr (at least one head)
0.75
iv. Pr (no heads) 0.25
2. A bag contains 1 red, 1 blue and 1 white marble. A marble is drawn from the bag, the color noted,
replaced and another marble is drawn.
a) Draw a tree diagram to represent the possible outcomes.
b) Calculate:
i. Pr(WW) 1/9 = 0.11
ii. Pr (not WW)
8/9 = 0.89
iii. Pr (at least one red) 5/9 = 0.56
iv. Pr (one red and one blue)
2/9 = 0.22 3. Heath and Jessica decide to play a game. In the first round Heath has a 0.65 chance of winning.
In the second round he doesn’t think as clearly and his chance of winning is 0.30.
a) Draw a tree diagram to represent two games played by Heath and Jessica.
b) List all the possible outcomes and their probability. HH = 0.65 x 0.3 = 0.195 HJ = 0.65 x 0.7 = 0.455 JH = 0.3 x 0.3 = 0.09 JJ = 0.3 x 0.7 = 0.21
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Independent Events 1. A pack of playing cards contains 26 red cards. As cards were selected, the result was recorded
and the card replaced. Calculate the following probabilities:
a) Pr (2 kings) 2/26 = 0.77
b) Pr (2 cards chosen are not picture cards)
18/26 = 0.69
c) Pr (first card is a picture card and the second is an even number) 8/26 x 10/26 = 0.30 x 0.38 = 0.114
2. A box contains 9 balls: 4 red, 2 blue, 3 green. If three balls are drawn, one at a time, and
replaced, calculate the following probabilities:
a) 3 green balls are chosen 3/9 x 3/9 x 3/9 = 0.036
b) the only red ball chosen is last
5/9 x 5/9 x 4/9 = 0.138
c) the first ball is blue, the second ball is green and the third ball is red 2/9 x 3/9 x 4/9 = 0.032
Dependent Events 1. A ‘lucky dip’ at a school fete contains 20 prizes, all of the same size. If 5 prizes are a set of
crayons, find the probability that, from the first 4 children to sample the dip:
a) the first 2 children receive crayons 5/20 x 4/19 x 15/18 x 14/17 = 0.036
b) no children receive crayons
15/20 x 14/19 x 13/18 x 12/17 = 0.28
c) 4 children receive crayons 5/20 x 4/19 x 3/18 x 2/17 = 0.001
2. A box contains 9 balls, 4 red, 2 blue, 3 green. If three balls are drawn one at a time without
replacement, calculate the following probabilities:
a) 3 green balls are chosen 3/9 x/ 2/8 x/ 1/7 = 0.012
b) the only red ball chosen is last
5/9 x/ 4/8 x/ 4/7 = 0.16
c) the first ball is blue, the second ball is green and the third ball is red 2/9 x 3/8 x 4/7 = 0.05
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