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5/16
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Do Now 5/16
Essential Question:
What is the difference
between independent
and dependent
events?
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Agenda
 Do
Now
 Good Things!!
 Recap:
 Experimental
vs Theoretical Probability
 Law of Large Numbers
 Notes:
 Independent
vs Dependent Events
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Good Things!!!
TEST WILL BE
OPEN NOTE
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Recap
 Probability
is always a number from 0 to 1
 Experimental
 Real
Probability
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
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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?
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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”
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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?
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Independent vs Dependent
• What does the word “independent” mean to you?
• What does the word “dependent” mean to you?
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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
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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!
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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?
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Independent Events
• 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!
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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)
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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
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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)
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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.
a) 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?
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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:
–
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Practice Problems
 www.problem-attic.com/test/r1arl6yp
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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.