Lesson 6 Handout

Complete the table.

Experiment Write the probability as a Fraction

Write the probability as a Decimal

Write the probability as a Percentage

There are 10 blue and 10 green cubes in a bag. What is the probability of drawing a green cube?

You open a telephone book and stick a pin on a number without looking. What is the probability of the number ending in a six?

You throw three dice. What is the probability that one of the numbers will be even?

You buy one ticket in a raffle. 100 tickets have been sold. What is the probability that your ticket will be drawn?

You need to throw a five to land on the next ladder in a Snakes and Ladders game. What is the probability of throwing a five?

There are five black, six red, five green, seven orange, four white and three yellow jelly babies in a packet. What is the probability of getting a yellow one?

You toss two coins. What is the probability that both coins will land heads up?

YouTube Clip 1 – Sample Space

Answer the following questions. Bold or underline your answers

1) What is your definition of sample space?

2) What 3 things did you notice all written examples have in common?

a) The outcomes are separated by a commab) The outcomes are separated by a full stopc) The outcomes are separated by a colond) The outcomes are shown inside a set of curly bracketse) The outcomes are shown inside explanation marksf) The outcomes are shown inside a set of parenthesesg) There is an equal sign used to show it is an answerh) There is a colon sign used to show it is an answer

YouTube Clip 2 – Describe Probabilities using Fractions, Decimals and Percentages.

Answer the following questions. Bold or underline your answers

1) What strategy do you use to convert a fraction into a decimal?

2) If you did not have a calculator, what could you do?

3) What is your definition of probability?

4) When writing probability as a fraction, what does the denominator refer to?

5) When writing probability as a fraction, what does the numerator refer to?

Lesson 6 Handout

Task 3 – Complete the table.

ExperimentWrite the sample space of possible

outcomes

SS = Sample SpaceProbability as a Fraction

Throwing a 5 on a dice

Drawing a red card from a deck of cards

Drawing a diamond from a deck of cards

Drawing a 10 from a deck of cards

Drawing a pink cube from a bag containing:

-4 red cubes

-4 yellow cubes

-4 green cubes

-4 purple cubes

-4 pink cubes

Spinning yellow on a spinner with 8 equal sized colours – red, blue, yellow, orange, green, purple, pink, black

Spinning green on a spinner with 5 equal sized colours – 2 red, 2 green, 1 black

Spinning green on a spinner with 10 equal sized colours – 4 red, 3 yellow, 2 green, 1 black

Worksheet One – Warm Up

Solve the problems below using your knowledge of probability. Write fractions in lowest terms.

Simple Chance Experiment Probability shown as a FractionWhat is the probability of choosing a king from a standard deck of playing cards? P =

What is the probability of choosing a green marble from a jar containing 5 red, 6 green and 4 blue marbles?

What is the probability of choosing a marble that is not blue in problem 2?

What is the probability of getting an odd number when rolling a single 6-sided die?

What is the probability of choosing a jack or a queen from a standard deck of 52 playing cards?

What is the probability of landing on an odd number after spinning a spinner with 7 equal sectors numbered 1 through 7?

What is the probability of getting a 7 after rolling a single die numbered 1 to 6?

What is the probability of choosing a queen, a king or an ace from a standard deck of playing cards?

What is the probability of choosing the letter i from the word probability?

What is the sample space for choosing a letter from the word probability? Sample Space: (

Probability Quiz

1. Place these three statements on the continuum to show their probability of occurring. Use the letters a, band c to represent each event.

a) If I throw two dice the numbers will add to seven.b) If I pick a card from a deck it will be hearts.c) If I toss a coin it will land on heads or tails.

2. Use letters to describe the likelihood of each event occurring.

Use I (Impossible), U (Unlikely), E (Equally likely), L (Highly likely) or C (Certain).

It will rain somewhere in Queensland tomorrow. ____________

If a dice is rolled, the number will be even. ____________

The school’s postcode is a four-digit number. ____________

Every student in the school likes cabbage. ____________

Every student in the class has two pets. ____________

3. Write an example of an event for each of the following likelihoods:

highly unlikely ______________________________________________________

highly likely ______________________________________________________

equally likely ______________________________________________________

4. List all the possible combinations of shirts and pants/skirts that could be worn. Use a tree diagram or organised list to help you.

Impo

ssib

le

Cer

tain

5. Anna does an experiment to see which face an empty cereal box is most likely to land on when it is tossed in the air. List (or draw) all the possible outcomes of the experiment.

6. A coin is being tossed. What is the probability that it will land on heads? Write your answer as a percentage. ____________

7. What is the probability of getting a two when you throw a dice? Write your answer as a fraction. ____________

8. What is the probability of drawing a blue ball from this bag?Write your answer as a decimal. ____________

Use this continuum to show the probability of drawing either a red or green ball from the bag.

9. Ezra tossed a dice 50 times and recorded the results in a frequency table. What was the relative frequency for the following numbers:

Fractions Decimal Percentage

2

4

5

10. The theoretical probability of throwing a six is 16 or 0.16. Is that what the

experimental data showed in the table in question 9? If not, explain why the two values might vary.

Handout 1 – Warm Up

Solve the problems below using your knowledge of probability. Write fractions in lowest terms.

Simple Chance Experiment Probability shown as a FractionWhat is the probability of choosing an ace from a standard deck of playing cards? P =

What is the probability of choosing a red marble from a jar containing 5 red, 6 green and 4 blue marbles?

What is the probability of choosing a marble that is not green in problem 2?

What is the probability of getting an even number when rolling a single 6-sided die?

What is the probability of choosing a queen or a king from a standard deck of 52 playing cards?

What is the probability of landing on an odd number after spinning a spinner with 9 equal sectors numbered 1 through 9?

What is the probability of getting a 0 after rolling a single die numbered 1 to 6?

What is the probability of choosing a picture card (jack, queen or king) from a standard deck of playing cards?

What is the probability of choosing the letter a from the word mathematics?

What is the sample space for choosing a letter from the word mathematics? Sample Space: (

.

Handout 2 – Quick Quiz

Select your answer by bolding or underlining the answer you think is correct

1. Which of the following is an experiment?a) Tossing a coin.b) Rolling a single 6-sided die.c) Choosing a marble from a jar.d) All of the above.

2. Which of the following is an outcome?a) Rolling a pair of dice.b) Landing on red.c) Choosing 2 marbles from a jar.d) None of the above.

3. Which of the following experiments does NOT have equally likely outcomes?a) Choose a number at random from 1 to 7.b) Toss a coin.c) Choose a letter at random from the word SCHOOL.d) None of the above.

4. What is the probability of choosing a vowel from the alphabet?

2126

526

121 none of these

5. A number from 1 to 11 is chosen at random. What is the probability of choosing an odd number?

111

511

611 none of these

Lesson 8 - Theoretical and Experimental Probability

A number cube is rolled 24 times and lands on 2 four times and on 6 three times.

a. Find the experimental probability of landing on a 2. b. Find the experimental probability of not landing on a 6. c. Compare the experimental probability you found in part a to its theoretical

probability.

_________________________________________________________________________d. Compare the experimental probability you found in part b to its theoretical

probability.

___________________________________________________________________________

Use the results of the survey in the table shown below. a. What is the probability that someone in the survey considered reading books or

surfing the Internet as the best entertainment value? Write the probability as a fraction.

b. Out of 500 people surveyed, how many would you expect considered reading books or surfing the Internet as the best entertainment value?

_____________________________________________________________________

c. Out of 300 people surveyed, is it reasonable to expect that 30 considered watching television as the best entertainment value? Why or why not?

3. A spinner marked with four sections blue, green, yellow, and red was spun 100 times. The results are shown in the table.

a. Find the experimental probability of landing on green. b. Find the experimental probability of landing on red. c. If the spinner is spun 50 more times, how many of these times would you expect the pointer to land on blue?

___________________________________________________________________________

4.

What is the probability that a student’s favourite hobby is roller skating?

Suppose 200 seventh-grade students were surveyed. How many can be expected to say that roller skating is their favourite hobby?

Suppose 60 seventh-grade students were surveyed. How many can be expected to say that bike riding is their favourite hobby?

Suppose 150 seventh-grade students were surveyed. How many can be expected to say that playing sports is their favourite hobby?

Lesson 9 Handout – Warm Up

Circle or bold the correct answer. Make your own multiple choice question in the last box.

Which of the following is a certain event?

Choosing a teacher from a room full of students.

Choosing an odd number from the numbers 1 to 10.

Getting a 4 after rolling a single 6-sided die.

None of the above.

There are 4 parents, 3 students and 6 teachers in a room. If a person is selected at random, what is the probability that it is a teacher or a student?

9/13

4/13

7/13

None of the aboveWhat is the probability that a single card chosen from a deck is not an ace?

4/52

48/52

39/52

None of the above.

Which of the following is the sample space when 2 coins are tossed?

{H, T, H, T}

{H, T}

{HH, HT, TH, TT}

None of the aboveA large basket of fruit contains 3 oranges, 2 apples and 5 bananas. If a piece of fruit is chosen at random, what is the probability of getting an orange or a banana? 4_over_5

1_over_2

7_over_10

None of the above.

Which of the following is the sample space for choosing a letter from the word LIBRARY?

{I, A}

{L, I, B, R, A, R, Y}

{L, I, B, R, A, Y}

None of the above

Which of the following is an impossible event?

Choosing an odd number from 1 to 10.

Getting an even number after rolling a single 6-sided die.

Choosing a white marble from a jar of 25 green marbles.

None of the above.

Experimental Probability

Use the information in the frequency table to calculate the experimental probability (relative frequency) of getting an even number when you throw a dice.

Fraction _______________ Decimal _______________ Percentage _______________

What is the theoretical probability of drawing a spade from a deck of cards? _______________

Draw a card from a deck of cards 25 times and write the results in the frequency table below. Replace the card and reshuffle each time .

What is the experimental probability (relative frequency) of drawing a club?

Fraction _______________ Decimal _______________ Percentage _______________

Using the table in the first box, calculate the experimental probability of throwing a four on a dice and then mark that probability on the continuum.

Experimental probability of throwing a four _______________

0 1

Chance Challenge

There are five challenges on this sheet. Each one involves the probability or chance of something happening. Decide how to find the solution to each challenge. Show the steps you use to find your solutions. If you need more space, work on a separate sheet of paper and attach it to this sheet.

1. Sam thinks that if he spells there/they’re/their as ‘t-h-e-r-e’ every time he writes it, the probability of him being correct is very high. Prove whether Sam’s thinking is correct.

2. Design a spinner with the following theoretical probabilities: 0.6 chance of landing on blue; 15

chance of landing on red and 20% chance of landing on green.

3. Choose a simple board game where two people have an equal chance of winning (like Snakes and Ladders). Change the rules so one player has only about a 30% chance of winning.

4. Josie did an experiment that involved throwing a coin, then a dice. Then she repeated the experiment but threw the dice first then the coin. Use tree diagrams to show whether both experiments had the same possible outcomes.

5. If you threw two dice 50 times and found the difference between the two numbers, what answer is most likely to occur?