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Notes: Simulations Scenarios Scenario 3: A certain professor has eight keys, but he never recalls which one fits his office door lock. He places all of the keys on a table and randomly selects and tries one key at a time. If the key does not fit he places the key back in the original pile and then randomly selects another key. (yes, he is senile and probably teaches statistics-don't laugh that would be rude) Note: all the keys look the same and he is unable to tell which key he has already tried. Conduct a simulation to answer the following questions. Use the random number table below and conduct 20 trials. Clearly identify each trial on the table . (a ) Explain how you would conduct a simulation using the random number table provided below to estimate the number of keys the professor would need to try in the lock. ( b ) What is the expected number of tries needed for him to find the correct key? (c) What is the probability it will take more than 4 tries to find the right key? 64831 78558 25961 07610 75464 85326 34336 39840 24371 53548 01485 57845 11792 38659 92620 48253 05370 80411 65985 43392 21100 08763 37469 66583 52822 48990 03648 34861 54680 64791 31645 45552 78255 64794 21228 69707 38804 45687 85320 54654 76156 01853 97115 91205 92396 97645 18911 76701 29815 81029 06361 86378 33931 09331