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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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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
given that a sample is normally distributed with M=10 sd=8 determine
disscuss probability sampling
Discuss probability sampling
What is mean
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.
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
get 6
guidelines of designing a table
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/
Frequency find questions
Rimsha Reply
What is nominal variable
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Write short notes on, nominal variable, ordinal variable, internal variable, ratio variable.
P( /x-50/ less than or equal to 5 ) where mean =52 and Variance =25
Jay Reply
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the exploration and analysis of large data to discover meaningful patterns and rules
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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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District statistical officer
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Hello every one
sample survey is done by local government in each and every field.
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statistics is one of the tool that represents the falling and rising of any cases in one sheet either that is in population census whether forecast as well as economic growth
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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.
wouldn't be correct to remove fractions, saying a number is justified as probabilities can also be decimals between 0 and 1.
Saying "a number" will include it being a decimal which are themselves fractions in another form.
I will simply say a probability is a number in the range zero to one, inclusive.
How to delete an entry? This last one was a pocket print.
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chance of occurrence
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What is Statistic
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Statistic is the mean of the sample.
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.
what actually is the definition of range
Chinedu Reply
I need social statistics materials
the range of a set of data is the difference between the largest and smallest values
I need more explanation about cluster sampling

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