Question 1147140
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First of all, let me notice, that your questions (a), (b) and (c) are posed INCORRECTLY.

My EDITING to your questions is as follows.



    (a) What is the probability that a selected {{{highlight(cross(programmer))}}} <U>employee</U> knows both languages?
    (b) What is the probability that a selected {{{highlight(cross(programmer))}}} <U>employee</U> knows C/C++ but not Java?
    (c) What is the probability that a selected {{{highlight(cross(programmer))}}} <U>employee</U> knows only one of the two languages?


     The rest of questions (d), (e) and (f) are correct.
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<U>Solution</U>


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We are given  

    P(C) = 0.7,  P(J) = 0.6,  and  P(C U J) = 0.9.


Then   P(C &#8745; J) = P(C) + P(J) - P(C U J) = 0.7 + 0.6 - 0.9 = 0.4.



       Now I am in position to answer all questions, one after another.



(a)  This probability is  P(C &#8745; J) = 0.4.



(b)  This set is  C \ (C &#8745; J);  therefore,

     this probability is equal to  P(C) - P(C &#8745; J) = 0.7 - 0.4 = 0.3.



(c)  This probability is equal to  P(C U J) - P(C &#8745; J) = 0.9 - 0.4 = 0.5.



(d)  This probability is  P(C &#8745; J)/P(J) = {{{0.4/0.6}}} = {{{2/3}}}.



(e)  This probability is  P(C &#8745; J)/P(C) = {{{0.4/0.7}}} = {{{4/7}}}.



(f)  To answer first part, compare  P(C)*P(J) with P(C &#8745; J).

          They are different;  therefore, the answer is  "NO".


     To answer the second part,  compare  P(C &#8745; J) with 0 (zero, ZERO).

          They are different;  therefore, the answer is  "NO".
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