Do the Experiment: 1. Count out 40 mixed-color M&Ms® which is approximately one small bag’s worth. Choose these M&Ms® ra

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Do the Experiment: 1. Count out 40 mixed-color M&Ms® which
is approximately one small bag’s worth. Choose these M&Ms®
randomly. 2. Record the number of each color in Table 1, reserve in
cup for Experimental Portion. Table 1 Population Color Quantity
Color Quantity Yellow Brown Green Orange Blue Red Experimental
Portion 1. The experiment is to pick two M&Ms, one at a time.
Do not look at them as you pick them. 2. You will do two methods
(one with replacement and one without replacement), each 24 times.
3. Carefully follow the directions for each part and record the
information in Table 2. With Replacement 1. The first time through,
put the first M&M back into the container before picking the
second one. 2. Record how many of each set in the “With
Replacement” column of Table 2. After you record the pick, put both
M&Ms back. 3. Do this 24 times. Without Replacement 1. The
second time through, after picking the first M&M, do not
replace it in the container before picking the second one. Then,
pick the second one. 2. Record how many of each set in the “Without
Replacement” column section of Table 2. After you record the pick,
put both M&Ms back. 3. Do this a total of 24 times, also.  
Table 2 Empirical Results First Pull Second Pull How many using
“With Replacement” How many using “Without Replacement” Yellow
Yellow Yellow Green Yellow Blue Yellow Brown Yellow Orange Yellow
Red Green Yellow Green Green Green Blue Green Brown Green Orange
Green Red Blue Yellow Blue Green Blue Blue Blue Brown Blue Orange
Blue Red Brown Yellow Brown Green Brown Blue Brown Brown Brown
Orange Brown Red Orange Yellow Orange Green Orange Blue Orange
Brown Orange Orange Orange Red Red Yellow Red Green Red Blue Red
Brown Red Orange Red Red   Calculate the Theoretical Probabilities
1. Use the data from Table 1 to calculate the Theoretical
Probabilities in Table 3. 2. Write your answers as simplified
fractions or decimals rounded to 4 places. Table 3 Theoretical
Probabilities Theoretical Probabilities With Replacement Without
Replacement P(Red-Red) P(Red-Brown OR Brown-Red) P(Red THEN Green)
P(Green Second GIVEN Red First) P(No Yellows) P(Doubles, Both Same
Color) Calculate the Empirical Probabilities a. Use the data from
Table 2 to calculate the Empirical Probabilities in Table 4. b.
Write your answers as simplified fractions or decimals rounded to 4
places. Table 4 Empirical Probabilities Empirical Probabilities
With Replacement Without Replacement P(Red-Red) P(Red-Brown OR
Brown-Red) P(Red THEN Green) P(Green Second GIVEN Red First) P(No
Yellows) P(Doubles, Both Same Color)   Discussion Questions (answer
1, 2e, and g in complete sentences) 1. Why are the “With
Replacement” and “Without Replacement” probabilities different? 2.
Convert P(No Yellows) to decimal format for both Theoretical “With
Replacement” and for Empirical “With Replacement”. Round to four
decimal places. a. Theoretical “With Replacement”: P(No Yellows) b.
Empirical “With Replacement”: P(No Yellows) c. Are the decimal
values “close”? Choose an item d. Did you expect them to be closer
together or farther apart? Choose an item e. Why or Why not? f. If
you increased the number of times you picked two M&Ms to 240
times, would this cause the empirical and theoretical probabilities
to be closer together or farther apart? Choose an item g. How do
you know?