Question 1206756
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Suppose that you are performing the probability experiment of rolling one fair six-sided die. 
Let F be the event of rolling a four or a five. You are interested in how many times you need 
to roll the die in order to obtain the first four or five as the outcome.
• p = probability of success (event F occurs)
• q = probability of failure (event F does not occur)
(a) Find the values of p and q. (Enter exact numbers as integers, fractions, or decimals.)
(b) Find the probability that the first occurrence of event F (rolling a four or five) 
is on the second trial. (Round your answer to four decimal places.)
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<pre>
(a)  p = probability that " a four or a five" occurs (event F).  This probability is

         p = {{{1/6}}} + {{{1/6}}} = {{{2/6}}} = {{{1/3}}}.    


     q = probability that event F does not occur.  It is a complementary event to F.

         q = 1 - p = 1 - {{{1/3}}} = {{{2/3}}}.



(b)  Probability of (b) is 

         P = P(event F is not a first roll; event F is the second roll) = (1-p)*p = q*p = {{{(2/3)*(1/3)}}} = {{{2/9}}}.
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Solved.