Transcript Dependent events

Chapter 12 and 8-5
Notes
12-1 Frequency Tables, Line
Plots, and Histograms
Frequency Table: lists each data item with the
number of times it occurs.
Line Plot: displays data with X marks above a
number line.
Histogram: shows the frequencies of data items
as a graph.
12-1 Frequency Tables, Line Plots,
and Histograms
Range: _______
12-1 Frequency Tables, Line Plots,
and Histograms-answers
34 5 6 7
5 3 1 1 2
Range: _4______
12-1 Frequency Tables, Line Plots,
and Histograms
Range: _______
12-1 Frequency Tables, Line Plots,
and Histograms-answers
0 1 2 3 4
5 2 0 4 1
Range: 4
12-1 Frequency Tables, Line Plots,
and Histograms
12-1 Frequency Tables, Line Plots,
and Histograms-answers
12-3 Using Graphs to
Persuade
You can draw graphs of data in different
ways in order to give different impressions.
You can use a break in the scale on one or
both axes of a line graph or a bar graph. This
lets you show more detail and emphasize
differences. It can also give you a distorted
view of the data.
12-3 Using Graphs to
Persuade
12-3 Using Graphs to
Persuade-answers
1. American
Ampersand
2. Fossil Week
3. You might compare
lengths of the bars
without noticing the
break in the scale.
12-3 Using Graphs to
Persuade
12-3 Using Graphs to
Persuade-answers
12-2 Box-and-Whisker Plots
A box-and-whisker plot: displays the
distribution of data items along a number
line.
Quartiles: divide the data into four equal
parts. The median is the middle quartile.
12-2 Box-and-Whisker Plots
12-2 Box-and-Whisker Plotsanswers
98
80.5
118
12-2 Box-and-Whisker Plots
12-2 Box-and-Whisker Plotsanswers
13
4
21
8-5 Scatter Plots
Scatter Plot: a graph that shows the relationship
between two sets of data. Graph data as ordered
pairs to make scatter plots.
8-5 Scatter Plots
8-5 Scatter Plots
8-5 Scatter Plots-answers
Positive correlation
Negative correlation
No correlation
12-4 Counting Outcomes
and Theoretical Probability
To count possible outcomes you can use a tree
diagram.
12-4 Counting Outcomes and
Theoretical Probability-answers
To count possible outcomes you can use a tree
diagram.
6 choices AM, AN, BM, BN, CM, CN
8 choices, P1C1, P1C2, P2C1, P2C2, P3C1,
P3C2, P4C1, P4C2
12-4 Counting Outcomes
and Theoretical Probability
To count possible outcomes you can use a tree
diagram or count choices using the Counting
Principle.
Counting Principle: If there are m ways of making
one choice, and n ways of making a second choice,
then there are m * n ways of making the first choice
followed by the second.
12-4 Counting Outcomes
and Theoretical Probability
Use the Counting Principle to solve each problem.
12-4 Counting Outcomes
and Theoretical Probabilityanswers
Use the Counting Principle to solve each problem.
5 * 7 * 4 = 140 ways
4 * 13 * 9 = 468 combinations
12-4 Counting Outcomes
and Theoretical Probability
Theoretical Probability:
P(event) = number of favorable outcomes
number of possible outcomes
12-4 Counting Outcomes and
Theoretical Probability-answers
Theoretical Probability:
P(event) = number of favorable outcomes
number of possible outcomes
m1A, m1B, m1C, m2A, m2B, m2C, m3A,
m3B, m3C, m4A, m4B, m4C
3/12 simplified to 1/3
1/12
Use a tree diagram to find the sample space for tossing
two coins. Then find the probability.
P(two heads)
P(one tail, one head)
Use counting principle to help you find each
probability.
Choosing three winning lottery numbers when the
numbers are chosen at random from 1 to 30. Numbers can
repeat.
Answers
Use a tree diagram to find the sample space for tossing
two coins. Then find the probability.
P(two heads) – 1/4
P(one tail, one head) – 1/2
Use counting principle to help you find each
probability.
Choosing three winning lottery numbers when the
numbers are chosen at random from 1 to 30. Numbers can
repeat. 1/90
12-5 Independent and
Dependent Events
Independent events: events for which the
occurrence of one event does not affect the
probability of the occurrence of the other.
Probability of Independent Events:
P(A, then B) = P(A) * P(B)
12-5 Independent and
Dependent Events
Probability of Independent Events:
P(A, then B) = P(A) * P(B)
12-5 Independent and
Dependent Events-answers
Probability of Independent Events:
P(A, then B) = P(A) * P(B)
1/36
3/36 or 1/12
6/36 or 1/6
2/36 or 1/18
1/36
9/36 or 1/4
12-5 Independent and
Dependent Events
Dependent events: events for which the
occurrence of one event affects the probability of
the occurrence of the other.
Probability of Dependent Events:
P(A, then B) = P(A) * P(B after A)
12-5 Independent and
Dependent Events
Probability of Dependent Events:
P(A, then B) = P(A) * P(B after A)
12-5 Independent and
Dependent Events-answers
Probability of Dependent Events:
P(A, then B) = P(A) * P(B after A)
1/90
6/90 or 1/15
6/90 or 1/15
4/90 or 2/445
4/90 or 2/45
24/90 or 4/15
12-5 Independent and
Dependent Events
12-5 Independent and
Dependent Events-answers
Dependent, the total number of cards
has been reduced by 1
Independent, the possibilities on the
second roll are the same as on the first.
12-5 Independent and
Dependent Events
12-5 Independent and
Dependent Events-answers
8/100 or 2/25
9/100
12/100 or 3/25
6/100 or 3/50
20/72 or 5/18
12/72 or 1/6
20/72 or 5/18
20/72 or 5/18
Probability
 Probability - when outcomes are
equally likely
 Probability of an event = P(event) =
# of favorable outcomes
# of possible outcomes
1/6
1/4
1
5/6
3/4
0/6; 0
Finding Odds
 Think of probability as a part/whole = this
is called odds - this describes the
likelihood of an event
Odds in favor of an event =
# of favorable outcomes
# of unfavorable outcomes
Odds against an event =
# of unfavorable outcomes
# of favorable outcomes
3 to 2; 2 to 3
2 to 3 ; 3 to 2
12-7 Experimental
Probability
Experimental Probability: probability
based on experimental data.
Experimental Probability:
P(event) = __number of times an event occurs
number of times experiment is done
12-7 Experimental
Probability
12-7 Experimental
Probability-answers
17.6%; 12/68
16.2%; 11/68
13.2%; 9/68
25%; 17/68
0%; 0/68
77.9%; 53/68
12-7 Experimental
Probability
12-7 Experimental
Probability-answers
1/2
1/8
3/8
7/8
12-8 Random Samples and
Surveys
Population: group about which you want
information
Sample: part of population you use to make
estimates about the population. Larger the
sample, more reliable your estimates will be.
Random Sample: each member of the
population has an equal chance to be selected.
12-8 Random Samples and
Surveys
12-8 Random Samples and
Surveys-answers
320 students
352 students
200 students
192 students
12-8 Random Samples and
Surveys
12-8 Random Samples and
Surveys-answers
Views of people coming out of computer store may not represent
the views of other voters. Not a good sample because not random.
The city telephone book may cover more than one school district.
It would include people who do not vote. Not a good sample, does
not represent population.
Good sample. People selected at random.