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“Countries List by Continent.” Worldatlas, 2013. Available online at http://www.worldatlas.com/cntycont.htm (accessed May 2, 2013).

Chapter review

In this module we learned the basic terminology of probability. The set of all possible outcomes of an experiment is called the sample space. Events are subsets of the sample space, and they are assigned a probability that is a number between zero and one, inclusive.

Formula review

A and B are events

P ( S ) = 1 where S is the sample space

0 ≤ P ( A ) ≤ 1

P ( A | B ) = P ( A AND B ) P ( B )

In a particular college class, there are male and female students. Some students have long hair and some students have short hair. Write the symbols for the probabilities of the events for parts a through j. (Note that you cannot find numerical answers here. You were not given enough information to find any probability values yet; concentrate on understanding the symbols.)

  • Let F be the event that a student is female.
  • Let M be the event that a student is male.
  • Let S be the event that a student has short hair.
  • Let L be the event that a student has long hair.
  1. The probability that a student does not have long hair.
  2. The probability that a student is male or has short hair.
  3. The probability that a student is a female and has long hair.
  4. The probability that a student is male, given that the student has long hair.
  5. The probability that a student has long hair, given that the student is male.
  6. Of all the female students, the probability that a student has short hair.
  7. Of all students with long hair, the probability that a student is female.
  8. The probability that a student is female or has long hair.
  9. The probability that a randomly selected student is a male student with short hair.
  10. The probability that a student is female.
  1. P ( L′ ) = P ( S )
  2. P ( M OR S )
  3. P ( F AND L )
  4. P ( M | L )
  5. P ( L | M )
  6. P ( S | F )
  7. P ( F | L )
  8. P ( F OR L )
  9. P ( M AND S )
  10. P ( F )
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Use the following information to answer the next four exercises. A box is filled with several party favors. It contains 12 hats, 15 noisemakers, ten finger traps, and five bags of confetti.
Let H = the event of getting a hat.
Let N = the event of getting a noisemaker.
Let F = the event of getting a finger trap.
Let C = the event of getting a bag of confetti.

Find P ( N ).

P ( N ) = 15 42 = 5 14 = 0.36

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Find P ( C ).

P ( C ) = 5 42 = 0.12

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Use the following information to answer the next six exercises. A jar of 150 jelly beans contains 22 red jelly beans, 38 yellow, 20 green, 28 purple, 26 blue, and the rest are orange.
Let B = the event of getting a blue jelly bean
Let G = the event of getting a green jelly bean.
Let O = the event of getting an orange jelly bean.
Let P = the event of getting a purple jelly bean.
Let R = the event of getting a red jelly bean.
Let Y = the event of getting a yellow jelly bean.

Find P ( G ).

P ( G ) = 20 150 = 2 15 = 0.13

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Find P ( R ).

P ( R ) = 22 150 = 11 75 = 0.15

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Find P ( O ).

P ( O ) = 150 - 22 - 38 - 20 - 28 - 26 150 = 16 150 = 8 75 = 0.11

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Use the following information to answer the next six exercises. There are 23 countries in North America, 12 countries in South America, 47 countries in Europe, 44 countries in Asia, 54 countries in Africa, and 14 in Oceania (Pacific Ocean region).
Let A = the event that a country is in Asia.
Let E = the event that a country is in Europe.
Let F = the event that a country is in Africa.
Let N = the event that a country is in North America.
Let O = the event that a country is in Oceania.
Let S = the event that a country is in South America.

Questions & Answers

only asking what is hospital statistics
Suly Reply
What's the meaning Of statistic
Farouk Reply
The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
khama Reply
pls I want to know the characterize of mean
Trixie Reply
I want solution to; x,x+1,3.5,3.4 and 2.5 is 3.1. find the value of x
mean is nothing but average.
(x+x+1+3.5+3.4+2.5)/5=3.1 2x+10.4=3.1*5 x=(15.5-10.4)/2 x=2.55
How. Pls explain or break it down thanks
the sum of all five divided by the 5 which is the average is equal to 3.1 so you sum them, divide and equate to 3.1. then solve for X by making X the subject
Think of it as your grade, or gpa. how do you find the average of it?
nicely explained
What is the meaning of statistics and it's relevance in the social sciences
Icecool Reply
statistics is the branch of mathematics that using math& statistics theories to interpret data to information which is supporting the decision makers in social sciences and applied too. statistics is decision making science now aday
I want to slove this math
Enny Reply
I'm not seeing the Math problem?
the data below where from 1 miles. miles 1:8380, 8210,3836,7840,7910,7510,7720,7750,8100,7690 test wherever their difference is significance at 5% level with population of #8000.
me too
enny i don't see any math problems
hello my friend. how can you help me to solve math
help me the interquartile range and semi interquartile range of grouped data
what is the difference between macro and micro data?
Sani Reply
Macrodata consist of 'headcounts', Microdata contain data on individuals,
macro is a big business and micro is small business
macro means whole or big and micro means part or small therefore in relation to data, macro data will be big or whole data and micro data will be small or individual part of a data. for example taking the whole data of an organisation or economy that will be macro data and taking the data on employe
employees will be micro data
How to determine appropriate statistics tool for my data
Jayr Reply
You cannot know everything! Statistics is a vast subject so don’t be afraid to say that you don’t know. Ask others for help or look up information on the internet to help. Don’t assume that the student knows anything about the technique they are suggesting!
my class starts at February 4th
P is the probability that a given die shows even number. To test H0 : P =1/2 against H1 : P=1/3, following procedure is adopted. Toss the die twice and accept H0 if both times it shows even number. Find the probabilities of type I and type II errors
Loyolite Reply
what is statistics?
bilal Reply
what is data
It Is the collection, collation,Analysing Interpretation,and presentation of data....
statistics is a science that studies numerical values assigned to objects, attributes or variables in order to characterize and make the variables more meaningful.
statistics is the science of collection, analysis, Interpretation & presentation of numerical data
Numeric data
if you think about normal number and operations of math such as fractions and percent values, statisitics is when it comes down to it a lot of just that - counting and then fractions, then that data and those counts (and ratios)/fractions that were used or counted in one group will represent a pop.
An example is, lets say you are in charge of making large orders of supplies and that based on your need of X bricks = X feet of building - now thats the math, well stats is using that math in a way the next person making orders can base those orders of what they will need based on saying "in this
..case, when Bilal needed 75 feet of building walls that 150 bricks were used" - now, that helps to get one job done but if we then watch those jobs one at a time, and count that 5/5 times the count was 150 bricks total - the new person could order 150 bricks with a high probability of being right
If X is a Uniform random variable in [ -2, 2 ], find the pdf of Y X  and E Y[ ].
Kezang Reply
could you resend the question it is not clear after " the PDF of---" ?
ap kis year ki student ho
Mastrs ist year
I'm from 2nd year BHU
ap kis year ki student ho
I'm student of bs(hons) 1st year
tell me good definition of statistics?
I want to know statistics
Okosa Reply
why is data so important in statistics
Trixie Reply
want summary statistic on gender, age group, weight, and weight loss
are you asking question or looking for Solution
solution pls
1st convert gender and group to factor than use summary function It will give mean median and mode with other details
its a bit complicated could u bring it to my level of under standing
u know the question was put in a tabular form where we were to find the variable type, summary statistics and graph type of the given variables that's the gender,age group, weight and weight loss
if you see, gender and group are not numerical due to which they will not give you correct statistics
how you denote gender m or f
or t
ok tnk u
these are not numerical so you have to convert they as f=1; m=2; t=3 same thing you have to do with group or any variable which is character else you should drop them
from your calculation
oh OK tnk u
so pls why is data important in statistics
not only data correct data is imp
statistics works on data only
without data you can not summarize, can not predict future, can not establish relationship between two and more variables, can not prepare reports and make decisions on it
so I'll give example. suppose you want to open a restaurant and you have to choose one best location out of 5. then how you will decide which location is best for you
awww thank you pls
pls I want a brief note on observation, survey and experimentation way of obtaining data
please Tell me difference parameters and non parameter
can you tell me about the scopes of statistics?
plzzz answer me anyone .
Methods of Collecting Data Observation Observational studies allow researchers to document behavior in a natural setting and witness events that could not be produced in a lab.
Key Points Observation differs from most other forms of data collection in that the researcher does not manipulate variables or directly question participants. The advantages of observation include observing natural behavior, refining hypotheses, and allowing for observation of behavior that canno
 be produced in an artificial environment for ethical or practical reasons. The disadvantages of observation are that these studies do not produce quantitative data, do not allow for cause and effect statements, may be very time consuming, and can be prone to researcher bias.
Key Terms observational research: Research focusing on the observation of behavior outside of a laboratory setting. external validity: In research, whether or not study findings can be generalized to real world scenarios.
Surveys and Interviews Surveys are a low-cost option for gathering a large amount of data, but they are also susceptible to reporting bias.
Key Points The survey method of data collection is likely the most common of the four major research methods. The benefits of this method include low cost, large sample size, and efficiency.
The major problem with this method is accuracy: since surveys depend on subjects’ motivation, honesty, memory, and ability to respond, they are very susceptible to bias. A researcher must have a strong understanding of how to properly frame survey questions in order to gather reliable and relevant
Key Terms reliability: The degree to which a measure is likely to yield consistent results each time it is used. validity: The degree to which a measure is actually assessing the concept it was designed to measure. survey: A method for collecting qualitative and quantitative information about ind
individuals in a population.
Interviews Interviews are a type of qualitative data in which the researcher asks questions to elicit facts or statements from the interviewee. Interviews used for research can take several forms:
Informal Interview: A more conversational type of interview, no questions are asked and the interviewee is allowed to talk freely. General interview guide approach: Ensures that the same general areas of information are collected from each interviewee. Provides more focus than the conversational ap
approach, but still allows a degree of freedom and adaptability in getting the information from the interviewee. Standardized, open-ended interview: The same open-ended questions are asked to all interviewees. This approach facilitates faster interviews that can be more easily analyzed and compared
Closed, fixed-response interview (Structured): All interviewees are asked the same questions and asked to choose answers from among the same set of alternatives.
experiments An experiment involves the creation of a contrived situation in order that the researcher can manipulate one or more variables whilst controlling all of the others and measuring the resultant effects.
Boyd and Westfall1 have defined experimentation as: "...that research process in which one or more variables are manipulated under conditions which permit the collection of data which show the effects, if any, in unconfused fashion."
Experiments can be conducted either in the field or in a laboratory setting. When operating within a laboratory environment, the researcher has direct control over most, if not all, of the variables that could impact upon the outcome of the experiment
When experiments are conducted within a natural setting then they are termed field experiments. The variety test carried out by United Fruits on their Gros Michel and Valery bananas is an example of a field experiment.
parameter Parameters are factors or limits which affect the way that something can be done or made
Minhal didny get your question, can you please elaborate more
pls can u use mean n mode at the statistical summary pls
yes, statistical summary itself gives all value
but u didn't tell me the advantage and disadvantage of the experimental method
but you didn't tell me the advantage and disadvantage of experimental method
tell me to make a hosrogram of dicrete values
by using a sampling distribution? how to estimate the population mean using a ramdom variable n?
Jade Reply
what is the important of statistics
The “average increase” for all NASDAQ stocks is the:
da Reply

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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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