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?

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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

• $$\frac{16}{30}$$  

• $$\frac{12}{30}$$  

• $$\frac{10}{30}$$