5/16

Do Now 5/16 Essential Question: What is the difference between independent and dependent events?

Agenda Do Now Good Things!! Recap: Experimental vs Theoretical Probability Law of Large Numbers Notes: Independent vs Dependent Events

Good Things!!! TEST WILL BE OPEN NOTE

Recap Probability is always a number from 0 to 1 Experimental Probability Real life Theoretical Probability What should happen Law of Large Numbers More trials = more reliable estimate of probability Chance variation Random, outside variables that mess with our results

Review Problem Mariana chose a simple random sample of 25 students from the population of students taking language arts. Miguel chose a simple random sample of 50 students from the same population. Shelby and Shane then determined the mean grade point average of the students in each sample. Who has a more reliable estimate of the mean grade point average?

Sample Space and Events The sample space is all the possible outcomes of an experiment Let’s say we are picking a card from a deck. The sample space would be all the cards in the deck, which is 52 An event is the result of my experiment Flipping a coin → sample space is 2 (can either get heads, or tails) Lands on tails → my event is “tails”

Sample Space and Events You are holding a bag with 17 marbles. 10 are red, and 7 are green. a. What is the sample space? b. What is the probability of picking a green marble? c. What is the probability of picking a red marble?

Independent vs Dependent What does the word “independent” mean to you? What does the word “dependent” mean to you?

Independent Events Two events are independent if one event has no effect on the probability of the other event. It is raining and you are drinking Gatorade It is Wednesday and the walls are white Ms. G is a great cook and she is wearing a dress What is A and B? Union, intersection?

Independent Events Deck of cards 52 cards total in a deck, 4 of each suit What is my probability of drawing the King of Hearts? Let’s say I draw the King of Hearts and I leave the card on a table… now what is my probability of drawing the Queen of Diamonds? It’s no longer independent! The first event CHANGED the second one!

Independent Events “With replacement” is your clue that it’s independent again Deck of cards 52 in a deck, 4 of each suit What is my probability of drawing the King of Hearts? I replace the card by putting it BACK in the deck. Now… what is my probability of drawing the Queen of Diamonds?

Independent Events Independent Events P(A and B) = P(A) • P(B) If two events are independent, you can multiply their individual probabilities to find the probability that both events will occur. Independent Events P(A and B) = P(A) • P(B) If this does NOT work… then they aren’t really independent!

Independent Events Two cards are drawn from a 52-card deck, with replacement. What is the probability that both cards are face cards? a. Are these events independent? How do you know? b. How many face cards are there? (*next slide for visual) c. What is the probability of drawing a face card the first time? The second time? Solve for P(face card AND face card)

Dependent Events If events are dependent, then the outcome of one event changes the outcome of another event. You bought purple shoes, so you bought purple shoelaces to match You got sick, and then you went to the doctor You drew a King of Hearts, did not replace the card, and THEN drew a King of Diamonds Notation: We read this as “the probability of B given that A already happened

Dependent Events Two cards are drawn from a 52-card deck, without replacement. What is the probability that both cards are face cards? a. Are these events dependent? How do you know? b. How many face cards are there? c. What is the probability of drawing a face card the first time? The second time? Solve for P(face card AND face card)

Let’s Practice Ms. G has a bag of letter tiles. The bag contains 2 A’s, 3 E’s, and 2 R’s. She takes a tile, replaces it, and then takes a second tile. Are these events independent or dependent? b) What is the probability of Ms. G picking the letter E the first time AND picking the letter E the second time?

RECAP Independent Events One event has NO IMPACT on another event Key words: “with replacement” P(A and B) = P(A) • P(B) Dependent Events The first event DOES IMPACT the second event Key words: “without replacement” Notation:

Practice Problems www.problem-attic.com/test/r1arl6yp

Independent or Dependent? The Johnson family has 3 puppies. Which pair of events is independent? a. The youngest puppy is a female. Exactly 2 puppies are females. b. The middle puppy is a male. Exactly 2 consecutive puppies are males. c. The youngest puppy is a male. Exactly 2 consecutive puppies are females. d. The middle puppy is a female. At least 2 puppies are females.