Hint: What are the RESULTS of the experiment?? Name:________________________________________________________________________________Date:_____/_____/__________ Warm-UP QUIZ DAY! Fill-in-the-Blanks: Theoretical probability is what should happen (based on math), while _____________________ probability is what actually happens. As the number of trials increase, the experimental probability will come closer to the ____________________ probability. Short Answer: Scott is attempting a new skateboard trick. If he lands 6 out of 8 attempts, what is the experimental probability that he will land his next attempt? For the following situations, decide whether they describe an experimental OR theoretical probability situation. Place an “E” for experimental or a “T” for theoretical: SITUATION “E” or “T” If Gary played 12 games of Connect Four and won 10 of them, finding the probability that he win the the next game played. Finding the probability that Leslie will get a # greater than 3 with one roll of a number cube. Hint: What are the RESULTS of the experiment?? If a standard number cube is rolled 40 times, what is the expected number of times a “4” will land face up (round to nearest whole number)? (set up a proportion) Start your proportion with the probability of rolling a “4” in ONE roll . . .

Fundamental Counting Principle: Jenny spun the below spinner 40 times, and landed on green 12 times. Compare the experimental probability with the theoretical probability. Experimental Probability: Theoretical Probability: Compare: What ACTUALLY happened . . . To make easier, write probability for getting green in ONE SPIN! Fundamental Counting Principle: How many total outcomes for flipping a coin and rolling a number cube? How many unique three-letter codes exist if the choices are A, B, C, D, E, F, or G . . . and each letter can be repeated more than once? Compound Probability: If a number cube is rolled and the spinner shown is spun . . . P(2, red) = P(even #, yellow) = P(# > 4, blue)

“Compound Probability” NAME: __________________________________________________________________________________DATE:____/_____/__________ Math-7 extra classwork “Compound Probability” AFTER THE QUIZ . . . ANSWER SPACE (Place answers to questions 1-4 in the table below): 1. 2. 3. 4. ANSWER SPACE (Place answers to questions 5-10 in the table below): 5. 6. 7. 8. 9. 10.

To calculate the probability of compound, dependent events. Today’s Lesson: What: probability of compound, dependent events Why: To calculate the probability of compound, dependent events.

Vocabulary: Two events are ______________________________ when the outcome of one event does NOT affect the outcome of the other event. Two events are ______________________________ when the outcome of one event DEPENDS on the outcome of the other. In other words, the first event ____________________________ the outcome of the second event. independent dependent affects

Scenario dependent independent independent or Independent? Out of a bag of 20 marbles, calculating the probability of picking a red marble, setting it aside, and picking a green marble. When flipping a coin and rolling a die, calculating the probability of getting heads and a 4. Out of a bucket of tootsie pops, calculating the probability of picking a cherry, putting it back in the bucket, and then picking an orange. dependent independent independent

Scenario dependent independent independent or Independent? When flipping three coins at once, calculating the probability of getting three heads in a row. From a standard deck of cards, calculating the probability of picking a red Queen, keeping it, and then picking a black Jack. From a standard deck of cards, calculating the probability of picking a diamond, replacing the card, and picking the six of hearts. independent dependent independent

Trial without replacement . . . What if we did a Tootsie Pop pick, but did not put the tootsie pops back in the bucket?? TRIAL #1: Tootsie Pop Double- Pick Out of 20 “two-pick” trials, how many times will a grape AND a cherry get picked? The first pop will NOT be replaced. P(grape and cherry) 1) What do we need to know? # of grape:___ # of cherry:___ total # of pops: ___ 2) Theoretical Probability: Do the experiment (20 trials): 4) Experimental Probability: (what should happen) 4 𝟒 𝟐𝟎 x 𝟑 𝟏𝟗 = 𝟏𝟐 𝟑𝟖𝟎 or 𝟑 𝟗𝟓 3 20 3% (what actually happened)

Examples: What if we tried to pick two grapes in a row– without replacing the first grape (use same numbers from our experiment)?? 𝟒 𝟐𝟎 x 𝟑 𝟏𝟗 = 𝟏𝟐 𝟑𝟖𝟎 or 𝟑 𝟗𝟓

P(vowel, then consonant) P(two consonants in a row) Examples continued . . . Without replacing any letters, Jane will pick two letters from a bag containing the following choices: M-A-T-H-I-S-C-O-O-L Answer the following: a) P(M, then C) b) P(vowel, then consonant) 𝟏 𝟏𝟎 x 𝟏 𝟗 = 𝟏 𝟗𝟎 𝟒 𝟏𝟎 x 𝟔 𝟗 = 𝟐𝟒 𝟗𝟎 = 𝟒 𝟏𝟓 c) P(two vowels in a row) d) P(two consonants in a row) 𝟒 𝟏𝟎 x 𝟑 𝟗 = 𝟏𝟐 𝟗𝟎 = 𝟐 𝟏𝟓 𝟔 𝟏𝟎 x 𝟓 𝟗 = 𝟑𝟎 𝟗𝟎 = 𝟓 𝟏𝟓

homework IXL: CC.6 CC.7

END OF LESSON The next slides are student copies of the notes and/or handouts for this lesson. These were handed out in class and filled-in as the lesson progressed.

Math-7 NOTES Vocabulary: DATE: ______/_______/_______ What: probability of compound, dependent events Why: To calculate the probability of compound, dependent events. NAME: Vocabulary: Two events are ______________________________ when the outcome of one event does NOT affect the outcome of the other event. Two events are ______________________________ when the outcome of one event DEPENDS on the outcome of the other. In other words, the first event ____________________________ the outcome of the second event. Scenario Dependent or Independent? Out of a bag of 20 marbles, calculating the probability of picking a red marble, setting it aside, and picking a green marble. When flipping a coin and rolling a die, calculating the probability of getting heads and a 4. Out of a bucket of tootsie pops, calculating the probability of picking a cherry, putting it back in the bucket, and then picking an orange. When flipping three coins at once, calculating the probability of getting three heads in a row. From a standard deck of cards, calculating the probability of picking a red Queen, keeping it, and then picking a black Jack. From a standard deck of cards, calculating the probability of picking a diamond, replacing the card, and picking the six of hearts.

IXL: CC.6 and CC.7 Trial without replacement . . . What if we did a Tootsie Pop pick, but did not put the tootsie pops back in the bucket?? TRIAL #1: Tootsie Pop Double- Pick Out of 20 “two-pick” trials, how many times will a grape AND a cherry get picked? The first pop will NOT be replaced. P(grape and cherry) 1) What do we need to know? # of grape ____ # of cherry _____ total # of pops: ___ 2) Theoretical Probability: Do the experiment (20 trials): 4) Experimental Probability: (what should happen) (what actually happened) Examples: What if we tried to pick two grapes in a row – without replacing the first grape(using the above numbers for our tootsie pop bucket)?? Without replacing any letters, Jane will pick two letters from a bag containing the following choices: M-A-T-H-I-S-C-O-O-L Answer the following: a) P(M, then C) b) P(vowel, then consonant) c) P(two vowels in a row) d) P(two consonants in a row) IXL: CC.6 and CC.7

“Compound Probability” NAME: _______________________________________________________________________________ DATE: ______/_______/_______ Math-7 classwork “Compound Probability” Independent Events: If there is one Queen of Hearts in a deck of 52 shuffled cards, what is the probability of drawing the Queen of Hearts, putting it back in the deck (replacing it), shuffling the deck, and then drawing the same card again? If there are four kings and four jacks in a deck of 52 cards, what is the probability of drawing a king, putting it back in the deck (replacing it), shuffling the deck, and then drawing a jack? What is the probability of flipping heads on a coin and then flipping tails? What is the probability of rolling a 3 on a six-sided number cube, and then flipping heads on a coin? You have a bag of 10 marbles. Four are red and 6 are blue. What is the probability of drawing a red marble, putting it back in the bag, and then drawing another red marble? If there are four kings in a deck of 52 cards, what is the probability of drawing a king, putting it aside (without replacing), and then drawing another king? Each letter in the word “MATH” is written on a card and put into a bag. What is the probability of drawing the “A,” keeping it (not replacing), and then drawing the “H”? You have a bag of 10 marbles. Four are red and 6 are blue. What is the probability of drawing a red marble, putting it aside, and then drawing another red marble? You have a bag of 10 marble. Four are red and 6 are blue. What is the probability of drawing a blue marble, putting it aside (no replacement), and then drawing a red marble? In a deck of 52 cards, half are black and half are red. What is the probability of drawing a black card, putting it aside (without replacing), and then drawing a red card? Dependent Events:

More probability practice Careful! This is a mixture of INDEPENDENT and DEPENDENT events!