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.
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
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miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
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Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
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Jharna
continue..
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Jharna
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play therapy.
speech therapy.
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Jharna
results you'll get..
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Jharna
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