Chance

Chance Intro

Mrs Wallace

​ALL the possible outcomes.

​Sample space

​We would write:

​{1, 2, 3, 4, 5, 6}

​We would write:

​{H, T}

Poll

What is the sample space of the spinner shown.

• green, red, blue, yellow

• green, green, green, red, yellow, yellow, blue, blue

• not sure

Poll

What is the sample space of the spinner shown?

• 5

• 1, 2, 2, 2,

• 3

• 1, 2, 3

​Assigning probability

​We don't use the word PROBABILITY a lot. Instead we use Pr.

EXAMPLES: ​

Pr (heads)= probability of heads

​Pr(6)= probability of getting a 6

​pr(girl)= probability of a girl

​Probabilities are between 0 and 1.

​Yes! That means fractions, decimals and percentages

​You roll a normal 6 sided dice. What is the probability of getting a 3?

Poll

Rolling a normal 6 sided dice. Pr(4)= 

• $$\frac{1}{6}$$  

• 1

• $$\frac{5}{6}$$  

Poll

Rolling a normal 6 sided dice. Pr(4 or 6)= 

• $$\frac{1}{6}$$  

• 2

• $$\frac{2}{6}$$  

Poll

P(green)=

• 3

• $$\frac{3}{8}$$  

• $$\frac{1}{8}$$  

Poll

Rolling a normal 6 sided dice. Pr(not a 4)= 

• $$\frac{1}{6}$$  

• 5

• $$\frac{5}{6}$$  

Poll

P(not red)=

• 1

• $$\frac{1}{8}$$  

• $$\frac{7}{8}$$  

Poll

Pr(blue or yellow)=

• 4

• $$\frac{2}{8}$$  

• $$\frac{4}{8}=\ \frac{1}{2}$$  

​Complementary Events

​All the outcomes that we don't want.

​Complements are shown with a '

​Complementary Events - EXAMPLES

When the event is Heads, the complement is Tails

​

​

​When the event is Monday, Wednesday the complement is Tuesday, Thursday, Friday, Saturday, Sunday

​

​

​When the event is Hearts the complement is Spades, Clubs, Diamonds, Jokers

​

Poll

complement of rolling an even number

• 1, 2, 3

• 2, 4, 6

• 1, 3, 5

• 1, 2, 3, 4, 5, 6

• no idea

Poll

Complement of rolling a 2 or 3

• 2 or 3

• 1, 4, 5, 6

• 1, 3, 5, 6

• 1, 2, 3, 4, 5, 6

• no idea

Poll

Compliment of tails

• head

• tail

• he

• no idea

Poll

compliment of hearts or spades

• hearts and spades

• diamonds and hearts

• diamonds and clubs

• no

​Probability of complementary events

5 red marbles, 3 blue marbles and 2 black marbles are place into the bag.

Poll

Using the spinner shown, Pr(red')

• $$\frac{1}{8}$$  

• 1

• $$\frac{7}{8}$$  

• 7

• no

Poll

Using the spinner shown, Pr(blue')

• $$\frac{5}{8}$$  

• 3

• $$\frac{3}{8}$$  

• 5

• no idea

Poll

Using the spinner shown, Pr(blue' or yellow')

• $$\frac{5}{8}$$  

• 3

• $$\frac{3}{8}$$  

• 5

• no idea

Poll

Which statement has a probability of 0?

• spinning red 

• spinning black

• spinning blue

• spinning yellow

• no idea

Poll

This diagram is called a

• circle

• Venn diagram

• Cats and Dogs

• No idea

​Reading Venn Diagrams

Multiple Choice

The left circle means people have 

• cats

• Cats and Dogs

• dogs

• ne

• no idea

Multiple Choice

The right circle means people have 

• cats

• Cats and Dogs

• dogs

• neither cats or dogs

• no idea

Multiple Choice

Where the circles intersect means people have 

• cats

• Cats and Dogs

• dogs

• neither cats or dogs

• no idea

Multiple Choice

The outside of the circles means people have 

• cats

• Cats and Dogs

• dogs

• neither cats or dogs

• no idea

​How many people were surveyed?

​10+5+7+8=

​How many people own a cat?

​(how many people are in the cat circle)

​How many people own a dog?

​(how many people are in the dog circle)

​How many people own only a cat?

​How many people own only a dog?

​How many people own both a dog and a cat?

​How many people own either a dog or a cat?

​How many people own neither a dog or a cat?

Fill in the Blank

How many students were surveyed?

Fill in the Blank

How many students took Physics?

Fill in the Blank

How many students studied Maths?

Fill in the Blank

How many students only studied Maths?

Fill in the Blank

How many students only studied Physics?

Fill in the Blank

How many students studied both?

Fill in the Blank

How many students studied neither?

Probabilities in Venn Diagrams

​PE vs Band

Multiple Choice

Pr(Soft drink)

• 14

• 16

• $$\frac{14}{30}$$  

• $$\frac{16}{30}$$  

Multiple Choice

Pr(neither)

• 4

• 10

• $$\frac{4}{30}$$  

• $$\frac{10}{30}$$  

Multiple Choice

Pr(Juice)

• 12

• 10

• $$\frac{12}{30}$$  

• $$\frac{10}{30}$$  

Multiple Choice

Pr(Juice')

• 14

• $$\frac{16}{30}$$  

• $$\frac{12}{30}$$  

• $$\frac{10}{30}$$