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This module introduces the contingency table as a way of determining conditional probabilities.

A contingency table provides a way of portraying data that can facilitate calculating probabilities. The table helps in determining conditional probabilities quite easily. The table displays sample values in relation to two different variables that may be dependent or contingent on one another. Later on, we will use contingency tables again, but in another manner. Contingincy tables provide a way of portraying data that can facilitate calculating probabilities.

Suppose a study of speeding violations and drivers who use car phones produced the following fictional data:

Speeding violation in the last year No speeding violation in the last year Total
Car phone user 25 280 305
Not a car phone user 45 405 450
Total 70 685 755

The total number of people in the sample is 755. The row totals are 305 and 450. The column totals are 70 and 685. Notice that 305 + 450 = 755 and 70 + 685 = 755 .

Calculate the following probabilities using the table

P(person is a car phone user) =

number of car phone users total number in study = 305 755

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P(person had no violation in the last year) =

number that had no violation total number in study = 685 755

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P(person had no violation in the last year AND was a car phone user) =

280 755

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P(person is a car phone user OR person had no violation in the last year) =

( 305 755 + 685 755 ) - 280 755 = 710 755

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P(person is a car phone user GIVEN person had a violation in the last year) =

25 70 (The sample space is reduced to the number of persons who had a violation.)

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P(person had no violation last year GIVEN person was not a car phone user) =

405 450 (The sample space is reduced to the number of persons who were not car phone users.)

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The following table shows a random sample of 100 hikers and the areas of hiking preferred:

Hiking area preference
Sex The Coastline Near Lakes and Streams On Mountain Peaks Total
Female 18 16 ___ 45
Male ___ ___ 14 55
Total ___ 41 ___ ___

Complete the table.

Hiking area preference
Sex The Coastline Near Lakes and Streams On Mountain Peaks Total
Female 18 16 11 45
Male 16 25 14 55
Total 34 41 25 100
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Are the events "being female" and "preferring the coastline" independent events?

Let F = being female and let C = preferring the coastline.

  • P(F AND C) =
  • P(F) P(C) =

Are these two numbers the same? If they are, then F and C are independent. If they are not, then F and C are not independent.

  • P(F AND C) = 18 100 = 0.18
  • P(F) P(C) = 45 100 34 100 = 0.45 0.34 = 0.153

P(F AND C) P(F) P(C) , so the events F and C are not independent.

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Find the probability that a person is male given that the person prefers hiking near lakes and streams. Let M = being male and let L = prefers hiking near lakes and streams.

  • What word tells you this is a conditional?
  • Fill in the blanks and calculate the probability: P(___|___) = ___ .
  • Is the sample space for this problem all 100 hikers? If not, what is it?
  • The word 'given' tells you that this is a conditional.
  • P(M|L) = 25 41
  • No, the sample space for this problem is 41.
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Find the probability that a person is female or prefers hiking on mountain peaks. Let F = being female and let P = prefers mountain peaks.

  • P(F) =
  • P(P) =
  • P(F AND P) =
  • Therefore, P(F OR P) =
  • P(F) = 45 100
  • P(P) = 25 100
  • P(F AND P) = 11 100
  • P(F OR P) = 45 100 + 25 100 - 11 100 = 59 100
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Muddy Mouse lives in a cage with 3 doors. If Muddy goes out the first door, the probability that he gets caught by Alissa the cat is 1 5 and the probability he is not caught is 4 5 . If he goes out the second door, the probability he gets caught by Alissa is 1 4 and the probability he is not caught is 3 4 . The probability that Alissa catches Muddy coming out of the third door is 1 2 and the probability she does not catch Muddy is 1 2 . It is equally likely that Muddy will choose any of the three doors so the probability of choosing each door is 1 3 .

Door choice
Caught or Not Door One Door Two Door Three Total
Caught 1 15 1 12 1 6 ____
Not Caught 4 15 3 12 1 6 ____
Total ____ ____ ____ 1
  • The first entry 1 15 = ( 1 5 ) ( 1 3 ) is P(Door One AND Caught) .
  • The entry 4 15 = ( 4 5 ) ( 1 3 ) is P(Door One AND Not Caught) .

Verify the remaining entries.

Complete the probability contingency table. Calculate the entries for the totals. Verify that the lower-right corner entry is 1.

Door choice
Caught or Not Door One Door Two Door Three Total
Caught 1 15 1 12 1 6 19 60
Not Caught 4 15 3 12 1 6 41 60
Total 5 15 4 12 2 6 1
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What is the probability that Alissa does not catch Muddy?

41 60

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What is the probability that Muddy chooses Door One OR Door Two given that Muddy is caught by Alissa?

9 19

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You could also do this problem by using a probability tree. See the Tree Diagrams (Optional) section of this chapter for examples.
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Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
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what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
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50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
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definitely of physics
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how many start and codon
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what is field
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physics, biology and chemistry this is my Field
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field is a region of space under the influence of some physical properties
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what is ogarnic chemistry
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determine the slope giving that 3y+ 2x-14=0
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Another formula for Acceleration
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a=v/t. a=f/m a
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innocent
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pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
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Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
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No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
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like charges repel while unlike charges atttact
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What is specific heat capacity
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Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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