1.3 Improper driving is severe public threat, and one may meet with an accident if he/she drives to accident prone area without a proper driving skill. Suppose that in one trial (i.e. goes to accident prone area once) if he/she follows the proper driving rules the probability of being met with an accident is low: pf = 0.05; and if he/she breaks the rules the probability of being affected is high: pp = 0.3. Please solve the following questions based on what you have learnt in probability; please present the detailed derivation for the solution step by step (you can do the calculation by using MATLAB).
(1) one goes to accident prone area for 5 times, if he/she follows the driving rule in each time, what is the probability of NOT being affected by an accident? and what is the probability of being affected by an accident, where "being affected" means
being affected "at least once"; [3%]
(2) one goes to accident area for 5 times, if he/she breaks the driving rule in each time. what is the probability of NOT being affected? and what is the probability of being
(3) what is the ratio of the probability of NOT being affected in one trial for "following 1-pf the driving rule" over "breaking the driving rule": i.e. Ratio1= 1-pb
your answer; based on the results in (a) and (b) calculate what will the above ratio become when the number of trial is 10: Ratio1o = your answer. And what conclusion can be draw by comparing the ratios between 1 trial and 10 trials. [5%]
