1. Probability Grade 7: Make predictions, given a probability
Calculate the theoretical and experimental probability of two independent events
Grade 8:
Calculate the probability that an event will NOT occur
Determine how probability changes if given multiple trials
Success Criteria:
Represent probability in a variety of ways (e.g., tree diagrams, tables)
Express probability as a decimal, fraction, and percent
Describe real-world uses of probability
Use proper mathematical vocabulary

2. Theoretical vs. Experimental Probability
Theoretical probability – The likeliness that an event will happen based on all possible outcomes
P = # 𝐹𝑎𝑣𝑜𝑢𝑟𝑎𝑏𝑙𝑒 𝑂𝑢𝑡𝑐𝑜𝑚𝑒𝑠 # 𝑃𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑂𝑢𝑡𝑐𝑜𝑚𝑒𝑠
Experimental probability – The ratio of the number of times an event occurred to the total number of attempts

3. Representing Probability
Calculate the theoretical probability of “spinning” a 4. Express the probability as a decimal, percent and fraction.
P = # 𝐹𝑎𝑣𝑜𝑢𝑟𝑎𝑏𝑙𝑒 𝑂𝑢𝑡𝑐𝑜𝑚𝑒𝑠 # 𝑃𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑂𝑢𝑡𝑐𝑜𝑚𝑒𝑠
P = 3 8
P = 0.375
P = 37.5%

4. Probability of Independent Events
Independent Events – 2 or more events that do not affect the probability of one another (e.g., rolling a die and flipping a coin)
Theoretical Probability of Independent events can be represented using
Organized Tables
Tree Diagrams
Number Sentences

5. What is the probability of rolling a 4 and spinning red?
Organized Table:
SPINNER
ROLL THE DIE
Blue
Red
Green
Pink 1 2 3 4 5 6
P = 2/48
= 1/24

6. What is the probability of rolling a 4 and spinning red?
Tree Diagrams:
Red Red Green Green Pink Blue Blue Blue 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6
P = 2/48
= 1/24

7. What is the probability of rolling a 4 and spinning red?
Number Sentence:
P(spinning red & rolling 4) = P(Spinning Red)• P(rolling 4)
= • 1 6
= 1/24

8. Using Probability to Make Predictions
1) If the probability that it will rain each day of the week is 43%, how many days can you expect it to rain in the week?
43% x 7 days
= 0.43 x 7 days
= 3 days
2) Mr. Cartwright won a free coffee on 2 out of 7 Tim Hortons Roll Up The Rim. How many free coffees would he expect to win if he bought 30 coffees?
P(winning) = 2/7 =
He can expect to win approximately 9 times.
x 30
= 8.57

9. Probability an event will NOT occur
The criteria for winning a game is you must roll a 5 or 6, flip tails on a coin, and draw a heart from a deck of cards. Calculate the probability of losing the game.
P(not winning) = 1 – P(winning)
= 1 – ( 1 3 • • )
P(rolling 5 or 6) = 1/3
= 1 – ( 1 24 )
P(flipping tails) = 1/2 =
P(drawing a heart) = 1/4
= or %

10. Probability When Given Multiple Attempts
Calculate the probability of flipping heads on a coin if given 4 attempts H T
P = H T H T H H T T H T H T H T H T H T H T H T H T H T H T

11. Probability When Given Multiple Attempts
Calculate the probability of flipping heads on a coin if given 4 attempts
P(success on multiple attempts) = 1 – P(not being successful on all attempts)
= 1 – ( 1 2 • • • 1 2 )
= 1 – 1 16 =

12. What is the probability of rolling a 4 and spinning red if given 3 tries?
Pspinning red & rolling 4 w/ 3 tries = 1 – (Plosing1• Plosing2 • Plosing3)
= 1 – ( • • )
= 1 –
Plosing = 1 – Pwinning
= 1 – (1/4)• (1/6) =
= 1 – (1/24)
= 23/24