The student will use theoretical and empirical methods to estimate probabilities.
The student will appraise the differences between the two estimates.
The student will demonstrate an understanding of long-term relative frequencies.
Do the experiment
Count out 40 mixed-color M&Ms® which is approximately one small bag’s worth. Record the number of each color in
[link] . Use the information from this table to complete
[link] . Next, put the M&Ms in a cup. The experiment is to pick two M&Ms, one at a time. Do
not look at them as you pick them. The first time through, replace the first M&M before picking the second one. Record the results in the “With Replacement” column of
[link] . Do this 24 times. The second time through, after picking the first M&M, do
not replace it before picking the second one. Then, pick the second one. Record the results in the “Without Replacement” column section of
[link] . After you record the pick, put
both M&Ms back. Do this a total of 24 times, also. Use the data from
[link] to calculate the empirical probability questions. Leave your answers in unreduced fractional form. Do
not multiply out any fractions.
Population
Color
Quantity
Yellow (
Y )
Green (
G )
Blue (
BL )
Brown (
B )
Orange (
O )
Red (
R )
Theoretical probabilities
With Replacement
Without Replacement
P (2 reds)
P (
R1B2 OR
B1R2 )
P (
R1 AND
G2 )
P (
G2 |
R1 )
P (no yellows)
P (doubles)
P (no doubles)
Note
G2 = green on second pick;
R1 = red on first pick;
B1 = brown on first pick;
B2 = brown on second pick; doubles = both picks are the same colour.
Empirical results
With Replacement
Without Replacement
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )
Empirical probabilities
With Replacement
Without Replacement
P (2 reds)
P (
R1B2 OR
B1R2 )
P (
R1 AND
G2 )
P (
G2 |
R1 )
P (no yellows)
P (doubles)
P (no doubles)
Discussion questions
Why are the “With Replacement” and “Without Replacement” probabilities different?
Convert
P (no yellows) to decimal format for both Theoretical “With Replacement” and for Empirical “With Replacement”. Round to four decimal places.
Theoretical “With Replacement”:
P (no yellows) = _______
Empirical “With Replacement”:
P (no yellows) = _______
Are the decimal values “close”? Did you expect them to be closer together or farther apart? Why?
If you increased the number of times you picked two M&Ms to 240 times, why would empirical probability values change?
Would this change (see part 3) cause the empirical probabilities and theoretical probabilities to be closer together or farther apart? How do you know?
Explain the differences in what
P (
G1 AND
R2 ) and
P (
R1 |
G2 ) represent. Hint: Think about the sample space for each probability.
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.
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?
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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