WEEK 6: SrAnsncs EXTRA CREDIT: PROBABILITY Torres 1' Save the File with your Name in it, ie 220_W6EC_TEysteridocx 2' Make sure it is a Word Doc or PDF le to ensure readability, 3' Answer all parts in complete sentences and show all work or explain how you got the values. Student Learning Outcomes . 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 'equenciesi Do the Experiment: L 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 L 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 L The rst time through, put the rst 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, Aer you record the pick, put both M&Ms back. 3' Do this 24 times, Without Replacement L The second time through, aer picking the rst 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. Aer you record the pick, put bath MJLMS back 3. Do this a total of 24 times, also Calculate the Theoretical Probabilities Table 2 Empirical Results 1. Use the data from Table 1 to calculate the Theoretical Probabilities in Table 3. First Second How many using "With How many using "Without 2. Write your answers as simplified fractions or decimals rounded to 4 places. Pul Pull Replacement" Replacement" Yellow Yellow retical Probabilities Yellow Green With Without Yellow Blue Replacement Brown Theoretical Probabilities Replacement Yellow Yellow Orange P(Red-Red) Yellow Red Green Yellow P(Red-Brown OR Brown-Red) Green Green P(Red THEN Green) Green Blue Green Brown P(Green Second GIVEN Red First) Green Orange Green Red P(No Yellows) Blue Yellow P(Doubles, Both Same Color) Blue Green Blue Blue te the Empirical Probabilities Blue Brown a. Use the data from Table 2 to calculate the Empirical Probabilities in Table 4. Blue Orange b. Write your answers as simplified fractions or decimals rounded to 4 places. Blue Red Brown Yellow Table 2 Empirical Probabilities Brown Green With Without Blue Empirical Probabilities Replacement Replacement Brown Brown Brown Brown Orange P(Red-Red) Brown Red P(Red-Brown OR Brown-Red) Orange Yellow Orange Green P(Red THEN Orange Blue P(Green Second GIVEN Red First) Orange Brown Orange Orange P(No Yellows) Orange Red Red Yellow P(Doubles, Both Same Color) Red Green Red Blue Red Brown Red Orange Red RedDiscussion Questions (answer 1, 2e, and g in complete sentences) 1. 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. 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 Choose an item ogether or farther apart? . 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 Choose an item theoretical probabilities to be closer together or farther apart? g. How do you know