You know relative frequency andtheoretical probability.

Written Assignment:

You are to write a report and show all your calculation for full credit. Then you will upload your report. Write neatly and work in sequential order. Please answer the following questions in order:

Experiment

1. Count out 40 mixed-color M&Ms which is approximately one small bag's worth. Record the number of each colour in Table 1 .
2. Use the quantity information from this Table 1 to complete the theoretical probabilities in Table 2 .
3. Next, put the M&Ms in a cup.
4. The experiment is to pick two M&Ms, one at a time. Donot look at them as you pick them.
5. The first time through, replace the first M&M before picking the second one. Record the results in the "With Replacement" column of Table 3 . Do this 24 times.
6. The second time through, after picking the first M&M, donot replace it before picking the second one. Then, pick the second one. Record the results in the "Without Replacement" column section of Table 3 . After you record the pick, putboth M&Ms back. Do this a total of 24 times, also.
7. Use the experimental data from Table 3 to calculate the empirical (experimental) probability questions in Table 4.

Record all probabilities as fractions and decimals.

TablesTable 1 Population

Color	Quantity
Yellow (Y)
Green (G)
Blue (BL)
Brown (B)
Orange (O)
Red (R)

Table 2 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.

Table 3 Empirical Results

With Replacement	Without Replacement
( __ , __ ) ( __ , __ )	( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )	( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )	( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )	( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )	( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )	( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )	( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )	( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )	( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )	( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )	( __ , __ ) ( __ , __ )
( __ , __ ) ( __ , __ )	( __ , __ ) ( __ , __ )

Table 4 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

1. Why are the "With Replacement" and "Without Replacement" probabilities different?
2. Compare P(no yellows) for both Theoretical "With Replacement" and for Empirical "With Replacement". Are the decimal values "close"? Did you expect them to be closer together or farther apart? Why?
3. If you increased the number of times you picked two M&Ms to 240 times, why would empirical probability values change?
4. Would this change (from part 3) cause the empirical probabilities and theoretical probabilities to be closer together or farther apart? How do you know?
5. Explain the differences in what P(G₁ AND R₂) and P(R₁|G₂) represent. Hint: Think about the sample space for each probability.