Math I UNIT QUESTION: How do you use probability to make plans and predict for the future? Standard:...
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Math I UNIT QUESTION: How do you use probability to make plans and predict for the future? Standard: MM1D1-3 Today’s Question: How can I find the different ways to arrange the letters in the word “PENCIL”?
Math I UNIT QUESTION: How do you use probability to make plans and predict for the future? Standard: MM1D1-3 Today’s Question: How can I find the different
Math I UNIT QUESTION: How do you use probability to make plans
and predict for the future? Standard: MM1D1-3 Todays Question: How
can I find the different ways to arrange the letters in the word
PENCIL? Standard: MM1D1.b.
Slide 2
Started out with the small diagnostic Then showed the video
What is Probability from the web site: www.learner.org
Slide 3
How many ways can four airlines fly two sizes of jets to three
cities?
Slide 4
Multiplication Counting Rule (Make a Tree Diagram) 4 times 2
times 3 = 24
Slide 5
There are 20 candidates for three different executive
positions. How many ways are there of filling the positions? How
many options do you have on the first pick? How many options do you
have for the second pick? (Answer: 20) (Answer: 19)
Slide 6
(Answer: 20 times 19 times 18 equals 6,840) How many options do
you have for the third pick? What is the total number of options?
(Answer: 18)
Slide 7
How many unique 5 digit security codes can be made from the
numbers 0 9 if we allow the numbers to be repeated? (Answer: 10 *
10 * 10 * 10 * 10 = 10^5 = 100,000)
Slide 8
How many unique 5 digit security codes can be made from the
numbers 0 9 if we do not allow the numbers to be repeated? (Answer:
10 * 9 * 8 * 7 * 6 = 30,240)
Slide 9
How many ways are there to flip a coin 10 times? They could all
be heads You could have the first 9 tosses be heads, and the last
toss be a tail. Etc. How many sides of the coin do we have? How
many tosses do we have? How many ways? Answer: Draw the Tree
Diagram: 2 *2*2*2*2*2*2*2*2*2 = 2^10 = 1,024
Slide 10
Suppose there are five dangerous military missions, each
requiring one soldier. In how many different ways can five soldiers
from a squadron of 100 be assigned to these five missions? (Answer:
100 * 99 * 98 * 97 * 96 = 9,034,502,400)
Slide 11
Multiplication Counting Principle If one event can occur in m
ways and a second event can occur in n ways, the number of ways the
two event can occur in sequence is m times n.
Slide 12
Multiplication Counting Principle At a sporting goods store,
skateboards are available in 8 different deck designs. Each deck
design is available with 4 different wheel assemblies. How many
skateboard choices does the store offer? 32
Slide 13
Multiplication Counting Principle A father takes his son,
Marcus, to Wendys for lunch. He tells Marcus he can get a 5 piece
nuggets, a spicy chicken sandwich, or a single for the main entre.
For sides, he can get fries, a side salad, potato, or chili. And
for drinks, he can get a frosty, coke, sprite, or an orange drink.
How many options for meals does Marcus have? 48
Slide 14
Class Work Tree Diagram handout
Slide 15
A probability experiment is an action through which specific
results (counts, measurements, or responses) are obtained. The
result of a single trial in a probability experiment is an outcome.
The set of all possible outcomes of a probability experiment is the
sample space. An event consists of one or more outcomes and is a
subset of the sample space.
Slide 16
Classical (theoretical) Probability Classical (or theoretical)
probability is used when each outcome in a sample space is equally
likely to occur. The classical probability of a event E is given
by:
Slide 17
Empirical (or statistical) Probability Empirical (or
statistical) probability is based on observations obtained from
probability experiments. The empirical probability of an event E is
the relative frequency of event E.
Slide 18
If P = 0, then the event _______ occur. Probability If P = 1,
then the event _____ occur. It is ________ It is ______ So
probability is always a number between ____ and ____. impossible
cannot certain must 1 0
Slide 19
Law of Large Numbers As an experiment is repeated over and
over, the empirical probability of an event approaches the
theoretical (actual) probability of the event.
Slide 20
Complement of event E The complement of event E is the set of
all outcomes in a sample space that are not included in event E.
The complement of event E is denoted by E, and is read as E prime.
The probability of an event plus its complement has to equal
1.
Slide 21
All of the probabilities must add up to 100% or 1.0 in decimal
form. Complements Example: Classroom P (picking a boy) = 0.60 P
(picking a girl) = ____ 0.40 1.00
Slide 22
Experiment 1 Break class into groups of 2. Have one person spin
penny, and the other keep a record if the penny came up heads or
tails. Repeat 7 times. Calculate the probability of heads, P(h),
per group. Calculate the probability of heads, P(h), per the class.
These calculations are experimental probability.
Slide 23
Experiment 1 What is the theoretical probability of spinning a
head, P(h)? What is the sample space? What is the complement of
spinning a head? What is the theoretical probability of the
complement? What is the theoretical probability of the P(h) plus
the complement? Was the whole class experimental P(h) closer to the
theoretical probability or individual groups?
Slide 24
Experiment 2 Break class into groups of 2. Have one person roll
two die, and the other keep a record if the sum of the die. Repeat
10 times. Calculate the probability the sum was less than 5, P(sum
< 5), per group. Calculate the probability the sum was less than
5, P(sum < 5), per the class. What kind of probability is
this?
Slide 25
Experiment 2 What is the theoretical probability of the sum
being less than 5, P(sum < 5)? What is the sample space? What is
the complement of the sum was less than 5, P(sum < 5)? What is
the theoretical probability of the complement? What is the
theoretical probability of the P(sum < 5) plus the complement?
Was the whole class experimental P(sum < 5) closer to the
theoretical probability or individual groups?
Slide 26
Class Work Pg 340, # 1 13 all
Slide 27
Warm Up Make a tree diagram and list the results of a number
consisting of one of the numbers 1, 2, 3, and one of the letters a,
b, c. List the possible options Answer: (3 * 3) + (3 * 3) = 18
Slide 28
Multiplication Counting Rule We have been using the
Multiplication Counting Rule Use the multiplication rule when order
does not matter Examples: ordering a meal, picking people for
positions, etc.
Slide 29
Addition Counting Rule Use the Addition Rule for events when
order does matter You have to calculate the number of possibilities
of each order, and then add them together.
Slide 30
Addition Counting Rule If the possibilities being counted can
be divided into groups with no possibilities in common, then the
total number of possibilities is the sum of the numbers of
possibilities in each group.
Slide 31
Addition Counting Rule Calculate the number of ways to make a
model number if it has to have one number and one letter Answer: 10
* 26 + 10 * 26 = 520
Slide 32
Addition Counting Rule Calculate the number of ways to make a
three symbol model number if it has to have one number and two
letters and the letters can not repeat
Slide 33
Addition Counting Rule Answer: Number first (10 * 26 * 25) =
6,500 Number second: (26 * 10 * 25) = 6,500 Number third: (26 * 25
* 10) = 6,500 Sum: 6500 + 6500 + 6500 = 19,500
Slide 34
Addition Counting Rule Calculate the number of ways to make a
two symbol model number. One symbol has to be a number, the other
symbol can be a number or letter. Number first: 10 * 36 = 360
Number second: 26 * 10 = 260 Total: 360 + 260 = 620
Slide 35
Addition Counting Rule Calculate the number of ways to make a
two symbol model number. At most, one symbol has to be a number,
the other symbol can be a number or letter. Number first: 10 * 36 =
360 Number second: 26 * 10 = 260 Total: 360 + 260 = 620
Slide 36
Addition Counting Rule Calculate the number of ways to make a
three symbol (numbers and letters) model number if at least one
letter is used Letter first (26 * 36 * 36) = 33,696 Letter second:
(10 * 26 * 36) = 9,360 Letter third: (10 * 10 * 26) = 2,600 33,969
+ 9,360 + 2,600 = 45,656
Slide 37
Class Work: pg 340, # 10 & 11 Pg 341 # 10, and Handout #
4-13 4-26