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A box has two balls, one white and one red. We select one ball, put it back in the box, and select a second ball (sampling with replacement). Let T be the event of getting the white ball twice, F the event of picking the white ball first, S the event of picking the white ball in the second drawing.

  1. Compute P ( T ).
  2. Compute P ( T | F ).
  3. Are T and F independent?.
  4. Are F and S mutually exclusive?
  5. Are F and S independent?
  1. P ( T ) = 1 4
  2. P ( T | F ) = 1 2
  3. No
  4. No
  5. Yes
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References

Lopez, Shane, Preety Sidhu. “U.S. Teachers Love Their Lives, but Struggle in the Workplace.” Gallup Wellbeing, 2013. http://www.gallup.com/poll/161516/teachers-love-lives-struggle-workplace.aspx (accessed May 2, 2013).

Data from Gallup. Available online at www.gallup.com/ (accessed May 2, 2013).

Chapter review

Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. If two events are not independent, then we say that they are dependent.

In sampling with replacement, each member of a population is replaced after it is picked, so that member has the possibility of being chosen more than once, and the events are considered to be independent. In sampling without replacement, each member of a population may be chosen only once, and the events are considered not to be independent. When events do not share outcomes, they are mutually exclusive of each other.

Formula review

If A and B are independent, P ( A AND B ) = P ( A ) P ( B ), P ( A | B ) = P ( A ) and P ( B | A ) = P ( B ).

If A and B are mutually exclusive, P ( A OR B ) = P ( A ) + P ( B ) and P ( A AND B ) = 0.

E and F are mutually exclusive events. P ( E ) = 0.4; P ( F ) = 0.5. Find P ( E F ).

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J and K are independent events. P ( J | K ) = 0.3. Find P ( J ).

P ( J ) = 0.3

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U and V are mutually exclusive events. P ( U ) = 0.26; P ( V ) = 0.37. Find:

  1. P ( U AND V ) =
  2. P ( U | V ) =
  3. P ( U OR V ) =
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Q and R are independent events. P ( Q ) = 0.4 and P ( Q  AND  R ) = 0.1. Find P ( R ).

P ( Q AND R ) = P ( Q ) P ( R )

0.1 = (0.4) P ( R )

P ( R ) = 0.25

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Bringing it together

A previous year, the weights of the members of the San Francisco 49ers and the Dallas Cowboys were published in the San Jose Mercury News . The factual data are compiled into [link] .

Shirt# ≤ 210 211–250 251–290 290≤
1–33 21 5 0 0
34–66 6 18 7 4
66–99 6 12 22 5

For the following, suppose that you randomly select one player from the 49ers or Cowboys.

If having a shirt number from one to 33 and weighing at most 210 pounds were independent events, then what should be true about P (Shirt# 1–33|≤ 210 pounds)?

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The probability that a male develops some form of cancer in his lifetime is 0.4567. The probability that a male has at least one false positive test result (meaning the test comes back for cancer when the man does not have it) is 0.51. Some of the following questions do not have enough information for you to answer them. Write “not enough information” for those answers. Let C = a man develops cancer in his lifetime and P = man has at least one false positive.

  1. P ( C ) = ______
  2. P ( P | C ) = ______
  3. P ( P | C' ) = ______
  4. If a test comes up positive, based upon numerical values, can you assume that man has cancer? Justify numerically and explain why or why not.

  1. P ( C ) = 0.4567
  2. not enough information
  3. not enough information
  4. No, because over half (0.51) of men have at least one false positive text
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Given events G and H : P ( G ) = 0.43; P ( H ) = 0.26; P ( H AND G ) = 0.14

  1. Find P ( H OR G ).
  2. Find the probability of the complement of event ( H AND G ).
  3. Find the probability of the complement of event ( H OR G ).
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Given events J and K : P ( J ) = 0.18; P ( K ) = 0.37; P ( J OR K ) = 0.45

  1. Find P ( J AND K ).
  2. Find the probability of the complement of event ( J AND K ).
  3. Find the probability of the complement of event ( J AND K ).
  1. P ( J OR K ) = P ( J ) + P ( K ) − P ( J AND K ); 0.45 = 0.18 + 0.37 - P ( J AND K ); solve to find P ( J AND K ) = 0.10
  2. P (NOT ( J AND K )) = 1 - P ( J AND K ) = 1 - 0.10 = 0.90
  3. P (NOT ( J OR K )) = 1 - P ( J OR K ) = 1 - 0.45 = 0.55
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Questions & Answers

probability sampling
Rosy Reply
dicuss probability sampling
Rosy
given that a sample is normally distributed with M=10 sd=8 determine
Rosy
disscuss probability sampling
Rosy
Discuss probability sampling
Rosy
What is mean
Rosy
Probability sampling is based on the fact that every member of a population has a known and equal chance of being selected. For example, if you had a population of 100 people, each person would have odds of 1 out of 100 of being chosen. With non-probability sampling, those odds are not equal.
Willard
The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.  To calculate it:  • add up all the numbers, • then divide by how many numbers there are. Example: what is the mean of 2, 7 and 9? Add the numbers: 2 + 7 + 9 = 18 Divide by how many numbers, 3 you
Willard
get 6
Willard
guidelines of designing a table
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you can find that information on this website there is a lot of information. It's about interpreting what the concept of information & data you are getting from the graph and understanding how to read the graph and analyze the information. ***understandinggraphics.com/design/data-table-design/
Willard
Frequency find questions
Rimsha Reply
?
Rosy
What is nominal variable
olusola Reply
Write short notes on, nominal variable, ordinal variable, internal variable, ratio variable.
olusola
P( /x-50/ less than or equal to 5 ) where mean =52 and Variance =25
Jay Reply
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Mukesh Reply
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Josephine Reply
the exploration and analysis of large data to discover meaningful patterns and rules
Hussein
how do we calculate the median
All Reply
f(x)=cx(1-x)^4 as x range 4rm 0<=x<=1. Can someone pls help me find d constant C. By integration only..
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uses of statistics in Local Government
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Hi
Tamuno
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Qamar-ul-
How about population census
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Okoi
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syeda
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raghavendra
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syeda
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Aadil
statistic is a technique, and statistics is a subject
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PM Reply
Probability tells you the likelihood of an event happening. ... The higher the probability, the more likely it is to happen. Probability is a number or fraction between 0 and 1. A probability of 1 means something will always happen, and a probability of 0 means something will never happen...
La Reply
Saying it's a number between zero and one means it is a fraction so you could remove "or fraction" from you definition.
Carlos
wouldn't be correct to remove fractions, saying a number is justified as probabilities can also be decimals between 0 and 1.
Denzel
Saying "a number" will include it being a decimal which are themselves fractions in another form.
Carlos
I will simply say a probability is a number in the range zero to one, inclusive.
Carlos
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Carlos
How to delete an entry? This last one was a pocket print.
Carlos
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sky-D Reply
chance of occurrence
Sikander
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Muhd Reply
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Tahir
What is Statistic
ibrahim Reply
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guillio
format of the frequency distribution table
henry
what is pearson correlation coefficient indicates?
Eticha
Statistic is the mean of the sample.
Raman
can anyone determine the value of c and the covariance and correlation for the joint probability density function Fxy(x,y)=c over the range 0<x<5,0<y,and x-1<y<x-1.
Nuhu
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Chinedu Reply
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the range of a set of data is the difference between the largest and smallest values
La
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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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