Probability of compound events Today’s Lesson: What: Probability of compound events Why: . . . so I can create and analyze tree diagrams; discover and use the fundamental counting principle; and use multiplication to calculate compound probability. How: . . . by taking accurate notes, participating, and completing homework.

In your own words, explain how you calculate the probability of compound events?

Compound Probability involves MORE than one event! Vocabulary: Compound Probability- refers to probability of more than ____________ event. Tree Diagram– shows the total possible __________________ of an event. Fundamental Counting Principle– uses multiplication to determine the total possible outcomes when _________ than one event is combined. Calculating Compound Probability– may use a tree diagram OR may _________________ the first event TIMES the second event. one outcomes more MULTIPLY

Tree Diagrams: Tossing Two Coins: Total Outcomes: _____ 4 Coin 2 Heads Tails Tails Heads Total Outcomes: _____ 4

Tossing Three Coins: Total Outcomes: _____ 8 H T H T H T H T Coin 3 Heads _____ Tails H T H T Tails Heads _____ H T H T Total Outcomes: _____ 8

3) Tossing One Coin and One Number Cube: ____ 1 2 3 H 4 5 ____ 6 1 2 3 T 4 5 6 Total Outcomes: _____ 12

Chocolate or Vanilla Ice cream Sprinkles, Nuts, or Cherry Choosing a Sundae with the following choices (may only choose one from each category): Chocolate or Vanilla Ice cream Fudge or Caramel Sauce Sprinkles, Nuts, or Cherry Your turn to make a tree diagram . . . Total Outcomes: _____ 12 Do we have to use a tree diagram? Is there a shortcut??

3) Tossing one coin and one number cube: Yes, there is . . . The Fundamental counting principle ! We can multiply to determine the outcomes . . . Tossing two coins: Tossing three coins: Multiply the outcomes for EACH event . . . 4 8 3) Tossing one coin and one number cube: Spinning a spinner with eight equal regions, flipping two coins, and tossing one number cube: 12 192

5) The total unique four-letter codes that can be created with the following letter choices (each letter can be used more than once)-- A, B, C, D, E, and F: The total unique locker combinations for a four-digit locker code (using the digits 0 – 9): Choosing from 12 types of entrees, 6 types of side dishes, 8 types of beverages, and 5 types of desserts: 8) Rolling two number cubes: 1,296 10,000 2,880 36

36,864 ways to “dress” a whataburger . . . Fundamental counting principle in action . . . How?? Think about it. The # of bread choices, times the # of meat choices, times the # of topping choices, times the # of sauce choices, etc., etc. It adds up fast!

Experimental Probability: PROBABILITY TRIALS . . . TRIAL #1: Rolling Two Number Cubes Out of 20 trials, how many times will doubles occur– P(doubles)? 1) What do we need to know? # of doubles:____ total # of outcomes: ___ Theoretical Probability: Do the experiment (20 trials): 4) Experimental Probability: 6 (what should happen) 36 𝟔 𝟑𝟔 𝒐𝒓 𝟏 𝟔 (what actually happens)

Experimental Probability: PROBABILITY TRIALS . . . TRIAL #2 : Rolling a Number Cube and Flipping a Coin Out of 20 trials, how many times will heads and a # less than 3 occur– P(heads and a # < 3)? What do we need to know? favorable outcomes: _____ total outcomes: _____ Theoretical Probability: Do the experiment (20 trials): 4) Experimental Probability: 2 (what should happen) 12 𝟐 𝟏𝟐 𝒐𝒓 𝟏 𝟔 (what actually happens)

𝟏 𝟐 x 𝟏 𝟐 = 𝟏 𝟒 Compound Probability sample questions: When two coins are tossed, what is the probability of both coins landing on heads – P (H and H) ? We can draw a tree diagram to answer this. OR, we can use MULTIPLICATION to solve: 𝟏 𝟐 x 𝟏 𝟐 = 𝟏 𝟒 P(1st Event ) x P(2nd Event) 2) When a number cube is rolled and the spinner shown is spun, what is the probability of landing on an even # and orange– P(even # and orange) ? 𝟑 𝟔 x 𝟏 𝟓 = 𝟑 𝟑𝟎 𝒐𝒓 𝟏 𝟏𝟎

a) P(ace and a vowel) b) P(red card and a “T”) A card is drawn from a standard deck of cards and a letter is picked from a bag containing the letters M-A-T-H-E-M-A-T-I-C-S: a) P(ace and a vowel) b) P(red card and a “T”) 𝟒 𝟏𝟒𝟑 𝟏 𝟏𝟏 A bag contains 3 grape, 4 orange, 6 cherry, and 2 chocolate tootsie pops. Once a pop is picked, it is placed back into the bag: a) P(grape , then cherry) b) P(two oranges in a row) c) P(chocolate , then orange) 𝟐 𝟐𝟓 𝟏𝟔 𝟐𝟐𝟓 𝟖 𝟐𝟐𝟓

Wrap-it-Up/Summary: In your own words, explain how you calculate compound probability. Multiply the probability of the first event TIMES the probability of the second event!

END OF LESSON