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**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.

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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

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**Scenario dependent dependent independent 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. 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. dependent independent independent independent dependent independent

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**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) 2 𝟐 𝟐𝟓 x 𝟓 𝟐𝟒 = 𝟏𝟎 𝟔𝟎𝟎 or 𝟏 𝟔𝟎 5 25 (what actually happened)

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Examples: What if we tried to pick two grapes in a row– without replacing the first grape (use same numbers from our experiment)?? 𝟐 𝟐𝟓 x 𝟏 𝟐𝟒 = 𝟐 𝟔𝟎𝟎 or 𝟏 𝟑𝟎𝟎

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**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

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END OF LESSON The next slides are student copies of the notes for this lesson. These notes were handed out in class and filled-in as the lesson progressed. NOTE: The last slide(s) in any lesson slideshow (entitled “Practice Work”) represent the homework assigned for that day.

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**Math-7 classwork/ warm-up “Compound Probability”**

DATE: ______/_______/_______ NAME: ____________________________ Math-7 classwork/ warm-up “Compound Probability” ANSWER SPACE (Place answers to questions in the table below): 1. 2. 3. 4. ANSWER SPACE (Place answers to questions in the table below): 5. 6. 7. 8. 9. 10.

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**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.

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**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)

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**“Compound Probability”**

DATE: ______/_______/_______ NAME: ____________________________ 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:

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**Math-7 Practice/Homework**

NAME: _______________________________________________________________________________ DATE: ______/_______/_______ Math-7 Practice/Homework “Probability”

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