Vocabulary: Probability– expressed as a ratio describing the # of ___________________ outcomes to the # of _______________________ outcomes. Probability is measured on a scale from 0 – 1. Compound Probability– involves more than one ________________________ (like rolling two number cubes, three coins, picking two cards, etc.) Independent Events– when one event does ____________________ affect the outcome of another event. For example, when two coins are tossed, the result of the 2 nd coin does NOT depend on what the first coin lands on. Both coins have a 50% chance of landing on heads (or tails) no matter what. Math-8 NOTES DATE: ______/_______/_______ What: probability of independent events Why: To introduce probability and calculate the probability of compound, independent events. What: probability of independent events Why: To introduce probability and calculate the probability of compound, independent events. NAME: Review: Remember the Fundamental Counting Principle? It’s a way that we can use multiplication to know the total number of outcomes for more than one event. Here’s how it works: Example: Tossing one coin and rolling one die. How many total outcomes? Explanation: Well, there are __________ outcomes for the coin, and __________ outcomes for the die. Multiply the separate outcomes, and that’s the answer... Answer: There are __________ total outcomes. You try: How many outcomes for... 1)Tossing three coins: 2) Rolling two dice: 3) Rolling a die and picking a card from a standard deck:

1)A bag contains 7 blue, 5 purple, 12 red, and 6 orange marbles. Find each probability if you draw one marble at random from the bag. Write as a fraction in simplest form. a) P(purple) b) P(red or orange) c) P(not blue) 2)You roll a standard number cube (six sides numbered 1 – 6). After one roll, answer the following: a) P(3 or 4) b) P (even #) c) P(not 2) 3)Fill in the following information about a standard deck of cards: TOTAL # of Cards:_____ # of Hearts( ♥ ): _____ # of Diamonds(♦):_____ # of Clubs( ♣ ):_____ # of Spades(♠):_____ # of Red Cards:_____ # of Black Cards:_____ Cards in Each Suit: _______ Now, given the above, answer the following: a) P(Ace)b) P(red card)c) P(Red King)d) P(Club) 4)Given the spinner to the right, answer the following: a) P(5)b) P(odd #)c) P(2 or an odd #) SAMPLE Probability Questions:

what about more than one event?? Compound Probability Sample Questions: 1)When two coins are tossed, what is the probability of both coins landing on heads – P (H and H)? 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) 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)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, then grape) d) P( three chocolates in a row) 5)Three number cubes are rolled. What is the probability of rolling a 3, an even #, and a 6 -- P (3, even #, and 6) ?

PROBABILITY TRIALS 1)Trial One: Tootsie Pop Pick (2 Picks) Out of 20 Trials (2 picks each), how many times will a grape get picked twice – P(grape and grape)? The pops will be replaced after each pick. -Probability : -What is our percentage chance? - Results of experiment: - Did the results match what should have happened? 2) Trial Two: Rolling Two Number Cubes After 20 trials, how many times will an even # AND an odd # land face up? -- P(Even # and Odd #)? -Probability : -What is our percentage chance? - Results of experiment: - Did the results match what should have happened? 3)Trial Three: Rolling a Number Cube and Tossing a Coin After 20 trials, how many times will Heads and a # less than 3 occur– P (H and # less than 3)? -Probability : -What is our percentage chance? - Results of experiment: - Did the results match what should have happened?

There are 6 orange marbles, 2 red marbles, 3 white marbles, and 4 green marbles in a bag. Once a marble is drawn it is replaced. Find the probability of each outcome. 1. P (red, then white)2.P(white, then green)3.P(two oranges in a row) 4.P(two not white in a row)5. P(green, then not green)6. P(red, then orange, then green) There are 5 yellow marbles, 1 purple marble, 3 green marbles, and 3 red marbles in a bag. Once a marble is drawn, it is replaced. Find the probability of each outcome. 7. P (purple, then red)8. P(red, then green)9. P(two greens in a row) 10. P(two red in a row)11. P(a purple then green)12. P(red, then yellow, then red) DATE: ______/_______/_______NAME: ____________________________ A number cube is rolled and the spinner is spun. Find each probability. 13. P(2 and green triangle)14. P(an odd number and a circle) 15. P(a prime number and a quadrilateral) 16. P(a number greater than 4 and a parallelogram) A eight-sided die is rolled and the spinner is spun. Find each probability. 13. P(4 and yellow fruit or veggie)14. P(an odd # and a pumpkin) 15. P(a prime # and a red fruit or veggie) 16. P(a # greater than 4 and a blue fruit or veggie)

DATE: ______/_______/_______NAME:_____________________________________________________________________________