Probability of independent versus dependent compound events Today’s Lesson: What: Probability of independent versus dependent compound events Why: . . . so I can calculate the probability of both independent AND dependent, compound events. How: . . . by taking accurate notes, participating, and completing homework.

What is the difference between independent and 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

dependent independent independent Scenario 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

independent dependent independent Scenario 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

Without replacing any letters, Jane will pick two letters from a 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(H, then a vowel) c) P(two vowels in a row) 𝟏 𝟏𝟎 x 𝟏 𝟗 = 𝟏 𝟗𝟎 𝟏 𝟏𝟎 x 𝟒 𝟗 = 𝟒 𝟗𝟎 = 𝟐 𝟒𝟓 𝟒 𝟏𝟎 x 𝟑 𝟗 = 𝟏𝟐 𝟗𝟎 = 𝟐 𝟏𝟓

Wrap-it-Up/Summary: What is the difference between independent and dependent compound events? Independent events refer to when the first event has NO affect on the outcome of the second event. DEPENDENT events refer to when the first event DOES AFFECT the outcome of the second event!!

IXL: DD.6 . . . and a worksheet given in class. homework IXL: DD.6 . . . and a worksheet given in class.

END OF LESSON