Transcript Probability

Probability
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Lesson
6.2.1
Probability
California Standard:
What it means for you:
Statistics, Data Analysis, and
Probability 3.3
Represent probabilities as ratios,
proportions, decimals between 0
and 1, and percentages between
0 and 100 and verify that the
probabilities computed are
reasonable; know that if P is the
probability of an event, 1–P is the
probability of an event not
occurring.
You’ll learn about using
probability as a way to describe
how likely events are to happen.
Key words:
•
•
•
•
•
•
probability
chance
likely
percent
fraction
decimal
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Essential Questions:
Why is probability useful in everyday life?
Make a connection to other content areas also explore
probability?
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Probability
A lot of the time, you can’t say for sure whether or not one
particular event will happen. But you can often say how
good the chances are.
What are the
chances that
I will roll a six?
Probability is a way of using numbers to describe the
chance of an event happening.
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Vocabulary
Probability is a way of using
numbers to describe the chance of
an event happening.
EventWhen we say "Event" we mean one (or more) outcomes
that are possible.
Example Events:
Getting a Tail when tossing a coin is an event
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Probability
Some Events Are More Likely to Happen Than Others
People often talk about things that might happen,
using words like “chance,” “likely,” and “probability”:
“What is the probability it will snow today?”
“How likely is it that the school football team will win its next game?”
“What is the chance that you will go to a movie this weekend?”
Look at the line below and think about where your answer
would be for each of these questions.
Impossible
Very
unlikely
Fairly
unlikely
Even
chance
Quite
likely
Very
likely
Certain
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Probability
Guided Practice
Decide where you would put the chances of the following
events happening on this scale:
Impossible
Very
unlikely
Fairly
unlikely
Even
chance
Quite
likely
1. Leaves falling from the trees next fall.
2. Finding a live elephant in your bedroom
when you get home.
Very
likely
Certain
Certain
Very very unlikely
3. Winning a raffle if you have 1 out of 100 tickets.
Very unlikely
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Solution follows…
Probability
Guided Practice
Decide where you would put the chances of the following
events happening on this scale:
Impossible
Very
unlikely
Fairly
unlikely
Even
chance
Quite
likely
Very
likely
4. Winning a raffle if you have 99 out of 100 tickets.
Certain
Very likely
5. Winning a raffle if you have 1 out of 1,000,000 tickets.
Very very unlikely
6. A tossed coin landing on heads.
Even chance
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Solution follows…
Probability
Guided Practice
7. Put the events named in Exercises 1–6 in order,
from most likely to least likely.
1. Leaves falling from the trees next fall.
2. Finding a live elephant in your bedroom when you get home.
3. Winning a raffle if you have 1 out of 100 tickets.
4. Winning a raffle if you have 99 out of 100 tickets.
5. Winning a raffle if you have 1 out of 1,000,000 tickets.
6. A tossed coin landing on heads.
Most likely
1
4
6
3
5
2
Least likely
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Solution follows…
Probability
Probability Is a Way to Say How Likely an Event Is
In math, probability is a way of describing the chance
that an event will occur. Probability can be written using
fractions, decimals, or percents.
You can replace the words on the line below with numbers
that represent how likely an event is to occur:
Impossible
0 or 0%
Very
unlikely
Fairly
unlikely
Even
chance
1
or 50%
2
Quite
likely
Very
likely
Certain
1 or 100%
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Lesson
6.2.1
Probability
0%
50%
100%
0
1
2
1
A probability of 0 (or 0%) means that there is no chance.
A probability of 1 (or 100%) means that the event will
definitely happen.
1
A probability of (or 50%) means that the event
2
might happen, but there’s an equal chance that it won’t.
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Lesson
6.2.1
Probability
Guided Practice
Estimate the probability that each of the following things
will happen. Write your answers as percents.
8. It will go dark tonight.
100%
9. Your math teacher will turn into a pineapple.
0%
10. A 6th-grader from California chosen at random
will be a girl. About 50%
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Solution follows…
Probability
Guided Practice
Use the list of probabilities below to answer
Exercises 11–12.
1
2
5
8
0
25
10
10
11. Which of the probabilities above represents
an impossible event? 0
25
12. Which of the probabilities above represents
a certain event? 10
10
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Solution follows…
Probability
Probability Is Usually Calculated Exactly
There are many situations where you can say exactly
what the probability of an event is.
This isn’t the same as saying whether an event will definitely
(or not definitely) happen — it’s just a measure of how likely
the event is.
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Probability
Example
1
What is the probability of spinning
the color red on this spinner?
What is the probability of spinning
the color blue?
Solution
Spinning the color red is certain, so the probability is 1.
Spinning the color blue is impossible, so the probability is 0.
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Solution follows…
Probability
Example
2
What is the probability of spinning
the color blue on this spinner?
Solution
The blue section is one-fourth of the spinner.
So the probability of spinning the color blue is
1
= 0.25 = 25%
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If you spun the spinner lots of times, about one-fourth
of the spins would land on blue.
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Solution follows…
Probability
Guided Practice
Exercises 13–15 are about this spinner.
Find the probability of spinning
the colors below.
Write your answers as decimals.
13. Blue
Half the spinner is blue, so the probability
of spinning blue is one-half or 0.5.
14. Yellow
Half the spinner is yellow, so the probability
of spinning yellow is one-half or 0.5.
15. Pink
It is impossible to spin pink, so the probability is 0.
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Solution follows…
Probability
Guided Practice
In Exercises 16–18, find the probability of spinning
the color yellow on each of the following spinners.
Write your answers as fractions.
16.
17.
1
4
18.
1
3
1
5
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Solution follows…
Probability
Independent Practice
Each set of cards shown below is turned over and shuffled,
then one card is picked.
A.
B.
C.
D.
For each set of cards, find the probability of picking:
1. a triangle card
A:
1
4
B:
1
5
C: 0
2. a star card
D:
1
5
A:
1
4
B: 0
C: 1
D:
2
5
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Solution follows…
Probability
Independent Practice
A bag has 1 red, 1 blue, and 2 yellow marbles in it.
3. How many marbles are in the bag?
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4. How many marbles are red? 1
What is the probability of drawing a red marble?
5. How many marbles are blue? 1
What is the probability of drawing a blue marble?
1
4
1
4
6. How many marbles are yellow? 2
What is the probability of drawing a yellow marble?
1
2
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Solution follows…
Probability
Independent Practice
7. The probability of an event occurring is 3 .
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Which two values below represent this same probability?
3
0.375
375%
0.375%
37.5%
%
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8. The probability of an event occurring is 55%.
Which two values below represent this same probability?
0.55
55
11
55
5.5
100
100
20
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Solution follows…
Probability
Independent Practice
9. In a tiled hallway, kids are jumping from one tile to the
next. The probability of landing on a green tile is 60%.
What fraction of the hallway area is covered with
green tiles? 3
5
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Solution follows…
Probability
Round Up
Probability is useful because you can use it to
compare the chances of different events happening.
The event with the highest probability is the
most likely to occur.
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