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

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

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%

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

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

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

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 4 • 1 6 = 1/24

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 = 0.2857 He can expect to win approximately 9 times. 0.2857 x 30 = 8.57

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 • 1 2 • 1 4 ) P(rolling 5 or 6) = 1/3 = 1 – ( 1 24 ) P(flipping tails) = 1/2 = 23 24 P(drawing a heart) = 1/4 =0.958 or 95.8%

Probability When Given Multiple Attempts Calculate the probability of flipping heads on a coin if given 4 attempts H T P = 15 16 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

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 2 • 1 2 ) = 1 – 1 16 = 15 16

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 – ( 23 24 • 23 24 • 23 24 ) = 1 – 0.880136 Plosing = 1 – Pwinning = 1 – (1/4)• (1/6) = 0.1198 = 1 – (1/24) = 23/24