a) Describe how you could create an experiment to simulate a student taking a 10 question true/false quiz. b) Conduct your experiment using at least 10 trials to represent the 10 questions. Record the results. c) From your results, determine the experimental probability of the student passing the quiz (ie. obtain 5 or more correct) d) How could you change your experiment so the experimental results will be closer to the actual theoretical results?
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a) A good way to simulate this type of test-taking is to assign a 50/50 chance of getting a question right by pure guessing, which is accomplished by flipping a coin and assigning one side of the coin for "true" and th other side for "false". b) The experiment would proceed by taking the first question and flipping the coin and recording true or false for that particular question using the method outlined in part "a". You would repeat this for each question. c) The probability of passing would be determined by adding the probabilities of getting exactly 5, exactly 6, exactly 7, exactly 8, exactly 9, and exactly 10 right. Using the binolial theorem, this is: (10C5)(1/2)^10 + (10C6)(1/2)^10 + (10C7)(1/2)^10 + (10C8)(1/2)^10 + (10C9)(1/2)^10 + (10C10)(1/2)^10 That last expression was written out just in case you got that far with determining exact probabilities for independent trials. Independence is present because each question separate as are the coin flips. d) You can add more trials and still take "half or more correct" as the passing criteria. The results will more closely mirror reality because the law of large numbers will cause the experimental results to even out by taking more trials.
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You're quite welcome! Good luck in all of your studies!
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