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

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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
PopulationColorQuantityColorQuantityYellowBrownGreenOrangeBlueRedExperimental
Portion1. 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 Replacement1. 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 Replacement1. 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 ResultsFirst PullSecond PullHow many using “With
Replacement”How many using “Without
Replacement”YellowYellowYellowGreenYellowBlueYellowBrownYellowOrangeYellowRedGreenYellowGreenGreenGreenBlueGreenBrownGreenOrangeGreenRedBlueYellowBlueGreenBlueBlueBlueBrownBlueOrangeBlueRedBrownYellowBrownGreenBrownBlueBrownBrownBrownOrangeBrownRedOrangeYellowOrangeGreenOrangeBlueOrangeBrownOrangeOrangeOrangeRedRedYellowRedGreenRedBlueRedBrownRedOrangeRedRed
Calculate the Theoretical Probabilities1. 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 ProbabilitiesTheoretical
ProbabilitiesWith ReplacementWithout
ReplacementP(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 Probabilitiesa. 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 2 Empirical ProbabilitiesEmpirical ProbabilitiesWith
ReplacementWithout ReplacementP(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 itemd. Did you expect them to be closer together or
farther apart?Choose an iteme. 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 itemg. How do you know?