Probability Worksheet Name:MA 202Spring Semester 2004WARNING: You must SHOW ALL OF YOUR WORK. You will receive NO CREDITif you do not show your work.DUE: TUESDAY, 02 MARCH 20041. M&M’s – Experiment 1(a) Each student should select one M&M from his or her bag of M&M’s. As a classwe have now conducted experiments. Use these experiments toanswer the following questions.i. What is the empirical probability of selecting a yellow M&M from a bag ofM&M’s?ii. What is the empirical probability of selecting a red M&M from a bag ofM&M’s?iii. What is the empirical probability of selecting an orange M&M from a bag ofM&M’s?iv. What is the empirical probability of selecting a blue M&M from a bag ofM&M’s?v. What is the empirical probability of selecting a brown M&M from a bag ofM&M’s?vi. What is the empirical probability of selecting a green M&M from a bag ofM&M’s?(b) Each student should replace the M&M he or she selected. Then he or she shouldselect another M&M. As a class we have now conducted experi-ments. Use these experiments to answer the following questions.i. What is the empirical probability of selecting a yellow M&M from a bag ofM&M’s?ii. What is the empirical probability of selecting a red M&M from a bag ofM&M’s?iii. What is the empirical probability of selecting an orange M&M from a bag ofM&M’s?iv. What is the empirical probability of selecting a blue M&M from a bag ofM&M’s?v. What is the empirical probability of selecting a brown M&M from a bag ofM&M’s?vi. What is the empirical probability of selecting a green M&M from a bag ofM&M’s?1(c) Each student should perform the experiment three more times. As a class we havenow conducted experiments. Use these experiments to answer thefollowing questions.i. What is the empirical probability of selecting a yellow M&M from a bag ofM&M’s?ii. What is the empirical probability of selecting a red M&M from a bag ofM&M’s?iii. What is the empirical probability of selecting an orange M&M from a bag ofM&M’s?iv. What is the empirical probability of selecting a blue M&M from a bag ofM&M’s?v. What is the empirical probability of selecting a brown M&M from a bag ofM&M’s?vi. What is the empirical probability of selecting a green M&M from a bag ofM&M’s?(d) Each student should perform the experiment a total of twenty times. As a classwe have now conductedexperiments. Use these experiments toanswer the following questions.i. What is the empirical probability of selecting a yellow M&M from a bag ofM&M’s?ii. What is the empirical probability of selecting a red M&M from a bag ofM&M’s?iii. What is the empirical probability of selecting an orange M&M from a bag ofM&M’s?iv. What is the empirical probability of selecting a blue M&M from a bag ofM&M’s?v. What is the empirical probability of selecting a brown M&M from a bag ofM&M’s?vi. What is the empirical probability of selecting a green M&M from a bag ofM&M’s?(e) What is the empirical probability of selecting a red M&M or a yellow M&M?(f) What is the empirical probability of selecting a red M&M and a yellow M&M?Are these events mutually exclusive.(g) The M&M web site contains information on the actual color distribution ofM&M’s? How do our results compare with this distribution?(h) Discuss the Law of Large Numbers in relation to our experiments.2. M&M’s – Experiments 2 and 32(a) Experiment 2 – Each student should select two M&M’s from their bag of M&M’s.Be sure to select the M&M’s one at a time. Replace the first M&M before selectingthe second.i. Conduct this experiment ten times and record your results. (You will con-duct ten experiments here. You should replace the M&M’s between eachexperiment.)ii. What is the empirical probability that the first and second M&M’s you selectwill be red?iii. What is the empirical probability that the first and second M&M’s a memberof this class selects will be red? Are these events independent?iv. What is the empirical probability that the first M&M you select will be blueand second will be green?v. What is the empirical probability that the first M&M a member of this classselects will be blue and second will be green? Are these events independent?(b) Experiment 3 – Each student should select two M&M’s from their bag of M&M’s.Be sure to select the M&M’s one at a time. Do not replace the first M&M beforeselecting the second.i. Conduct this experiment ten times and record your results. (You will conductten experiments here. You should replace the M&M’s between each experi-ment. That is, you should select on M&M. Do not replace it. You should thendraw a second M&M. Record your results for the first and second M&M’s.Now put both M&M’s back in the bag since you have completed the firstexperiment. Proceed to conduct the second experiment.)ii. What is the empirical probability that the first and second M&M’s you selectwill be red?iii. What is the empirical probability that the first and second M&M’s a memberof this class selects will be red? Are these events independent?iv. What is the empirical probability that the first M&M you select will be blueand second will be green?v. What is the empirical probability that the first M&M a member of this classselects will be blue and second will be green? Are these events independent?3. Let A be the event that a person selected at random has blonde hair. Let B be theevent that a person selected at random has brown eyes. Are these events independent?Justify your answer.4. Do numbers 5,6,7,9,14, and 15 in section 10.1 of your textbook.5. What is The Addition Principle of Counting? Use a Venn diagram to explain thisprinciple.6. Cards.3(a) What is the sample space for drawing a card from an ordinary deck of cards?(b) In how many ways can you select a black card or a ten? Are these events mutuallyexclusive?(c) In how many ways can you select a two or a five? Are these events mutuallyexclusive?7. Dice(a) What is the sample space for rolling two dice?(b) In how many ways can you roll a seven or five? Are these events mutually exclu-sive?(c) In how many ways can you roll the dice so that the score is seven or at least oneof the dice shows a two? Are these events mutually exclusive?8. There are twenty-four students in this class.(a) In how many ways can we select a President, a Vice President, a Treasurer, anda Secretary for this class?(b) In how many ways can we select a four-member social committee for this class?How is this problem related to the previous