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.
Suppose a study of speeding violations and drivers who use cell phones produced the following fictional data:
Speeding violation in the last year
No speeding violation in the last year
Total
Cell phone user
25
280
305
Not a cell 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.
a. Find
P (Person is a car phone user).
a.
b. Find
P (person had no violation in the last year).
b.
c. Find
P (Person had no violation in the last year
was a car phone user).
c.
d. Find
P (Person is a car phone user
person had no violation in the last year).
d.
e. Find
P (Person is a car phone user
person had a violation in the last year).
e.
(The sample space is reduced to the number of persons who had a violation.)
f. Find
P (Person had no violation last year
person was not a car phone user)
f.
(The sample space is reduced to the number of persons who were not car phone users.)
Try it
[link] shows the number of athletes who stretch before exercising and how many had injuries within the past year.
Injury in last year
No injury in last year
Total
Stretches
55
295
350
Does not stretch
231
219
450
Total
286
514
800
What is
P (athlete stretches before exercising)?
What is
P (athlete stretches before exercising
no injury in the last year)?
P (athlete stretches before exercising) =
= 0.4375
P (athlete stretches before exercising
no injury in the last year) =
= 0.5739
[link] shows a random sample of 100 hikers and the areas of hiking they prefer.
Hiking area preference
Sex
The Coastline
Near Lakes and Streams
On Mountain Peaks
Total
Female
18
16
___
45
Male
___
___
14
55
Total
___
41
___
___
a. Complete the table.
a.
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
b. Are the events "being female" and "preferring the coastline" independent events?
Let
F = being female and let
C = preferring the coastline.
Find
.
Find
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.
b.
= 0.18
P (
F )
P (
C ) =
= (0.45)(0.34) = 0.153
≠
P (
F )
P (
C ), so the events
F and
C are not independent.
c. 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?
c.
The word 'given' tells you that this is a conditional.
P (
ML ) =
No, the sample space for this problem is the 41 hikers who prefer lakes and streams.
d. Find the probability that a person is female or prefers hiking on mountain peaks. Let
F = being female, and let
P = prefers mountain peaks.
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.
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?
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
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
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
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
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?
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?
Robert
like charges repel while unlike charges atttact
Raymond
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