Warm Up

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Preview
Warm Up
California Standards
Lesson Presentation
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Warm Up 1. If you roll a number cube, what are
the possible outcomes? 2. Add . 3. Add
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1, 2, 3, 4, 5, or 6
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(No Transcript)
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Vocabulary
theoretical probability equally
likely fair mutually exclusive disjoint events
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Theoretical probability is used to estimate
probabilities by making certain assumptions about
an experiment. Suppose a sample space has 5
outcomes that are equally likely, that is, they
all have the same probability, x. The
probabilities must add to 1.
x x x x x 1
5x 1
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A coin, die, or other object is called fair if
all outcomes are equally likely.
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Additional Example 1 Calculating Theoretical
Probability
An experiment consists of spinning this spinner
once. Find the probability of each event.
A. P(4)
The spinner is fair, so all 5 outcomes are
equally likely 1, 2, 3, 4, and 5.
number of outcomes for 4 5
P(4)
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Additional Example 1 Calculating Theoretical
Probability
An experiment consists of spinning this spinner
once. Find the probability of each event.
B. P(even number)
There are 2 outcomes in the event of spinning an
even number 2 and 4.
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Check It Out! Example 1
An experiment consists of spinning this spinner
once. Find the probability of each event.
A. P(1)
The spinner is fair, so all 5 outcomes are
equally likely 1, 2, 3, 4, and 5.
number of outcomes for 1 5
P(1)
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Check It Out! Example 1
An experiment consists of spinning this spinner
once. Find the probability of each event.
B. P(odd number)
There are 3 outcomes in the event of spinning an
odd number 1, 3, and 5.
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Additional Example 2 Calculating Probability for
a Fair Number Cube and a Fair Coin
An experiment consists of rolling one fair number
cube and flipping a coin. Find the probability of
the event.
A. Show a sample space that has all outcomes
equally likely.
The outcome of rolling a 5 and flipping heads can
be written as the ordered pair (5, H). There are
12 possible outcomes in the sample space.
1H 2H 3H 4H 5H 6H
1T 2T 3T 4T 5T 6T
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Additional Example 2 Calculating Theoretical
Probability for a Fair Coin
An experiment consists of rolling one fair number
cube and flipping a coin. Find the probability of
the event.
B. P(tails)
There are 6 outcomes in the event flipping
tails (1, T), (2, T), (3, T), (4, T), (5, T),
and (6, T).
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Check It Out! Example 2
An experiment consists of flipping two coins.
Find the probability of each event.
A. P(one head one tail)
There are 2 outcomes in the event getting one
head and getting one tail (H, T) and (T, H).
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Check It Out! Example 2
An experiment consists of flipping two coins.
Find the probability of each event.
B. P(both tails)
There is 1 outcome in the event both tails (T,
T).
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Additional Example 3 Altering Probability
Stephany has 2 dimes and 3 nickels. How many
pennies should be added so that the probability
of drawing a nickel is ?
Adding pennies to the bag will increase the
number of possible outcomes.
Set up a proportion. Let x equal the number of
pennies
Find the cross products.
3(5 x) 3(7)
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Additional Example 3 Continued
15 3x 21
Multiply.
Subtract 15 from both sides.
15 15
3x 6
Divide both sides by 3.
x 2
2 pennies should be added to the bag.
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Check It Out! Example 3
Carl has 3 green buttons and 4 purple buttons.
How many white buttons should be added so that
the probability of drawing a purple button is
?
Adding buttons to the bag will increase the
number of possible outcomes. Let x equal the
number of white buttons.
Set up a proportion. Let x equal the number of
white buttons.
Find the cross products.
2(7 x) 9(4)
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Check It Out! Example 3 Continued
14 2x 36
Multiply.
14 14
Subtract 14 from both sides.
2x 22
Divide both sides by 2.
x 11
11 white buttons should be added to the bag.
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Two events are mutually exclusive, or disjoint
events, if they cannot both occur in the same
trial of an experiment. For example, rolling a 5
and an even number on a number cube are mutually
exclusive events because they cannot both happen
at the same time.
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Additional Example 4 Finding the Probability of
Mutually Exclusive Events
Suppose you are playing a game in which you roll
two fair number cubes. If you roll a total of
five you will win. If you roll a total of two,
you will lose. If you roll anything else, the
game continues. What is the probability that the
game will end on your next roll?
It is impossible to roll both a total of 5 and a
total of 2 at the same time, so the events are
mutually exclusive. Add the probabilities to
find the probability of the game ending on your
next flip.
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Additional Example 4 Continued
P(game ends) P(total 2) P(total 5)
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Check It Out! Example 4
Suppose you are playing a game in which you flip
two coins. If you flip both heads you win and if
you flip both tails you lose. If you flip
anything else, the game continues. What is the
probability that the game will end on your next
flip?
It is impossible to flip both heads and tails at
the same time, so the events are mutually
exclusive. Add the probabilities to find the
probability of the game ending on your next flip.
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Check It Out! Example 4 Continued
P(game ends) P(both tails) P(both heads)
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Lesson Quiz
An experiment consists of rolling a fair number
cube. Find each probability. 1. P(rolling an odd
number) 2. P(rolling a prime number) An
experiment consists of rolling two fair number
cubes. Find each probability. 3. P(rolling two
3s) 4. P(total shown gt 10)