Question 1193151
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                    Solution to part  (c)



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P = P(stop1 stop2 no-stop3) + P(stop1 no-stop2 stop3) + P(no-stop1 stop2 stop3) = 

  =    0.4*0.8*(1-0.3)      +   0.4*(1-0.8)*0.3)      +  (1-0.4)*0.8*0.3        = 0.392    (exact value).    <U>ANSWER</U>
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Solution to part &nbsp;(d)



<pre>
It is the conditional probability P = {{{stop_at_the_second_set_of_light/given_that_he_has_to_stop_at_exactly_two_sets_of_light}}}.


The denominator  {{{P[denominator]}}}  is the probability that Zimmer will stop at exactly two lights:

we just found this expression and the value 0.392 in part (c).



The numerator is, OBVIOULSY,  

    {{{P[numerator]}}} = P(stop1 stop2 no-stop3) + P(no-stop1 stop2 stop3) = 

                       = 0.4*0.8*(1-0.3) + (1-0.4)*0.8*0.3 = 0.368  (exact value).



Now the <U>ANSWER</U> to this question is  P = {{{P[numerator]/P[denominator]}}} = {{{0.368/0.392}}} = 0.9388  (rounded).
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Solved.