SOLUTION: Among employees of a certain firm, 70% know C/C++, 60% know Java, and 90% know at least one of the two languages. (a) What is the probability that a selected programmer knows bot

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Question 1147140: Among employees of a certain firm, 70% know C/C++, 60% know Java, and 90% know at least one of the two
languages.
(a) What is the probability that a selected programmer knows both languages?
(b) What is the probability that a selected programmer knows C/C++ but not Java?
(c) What is the probability that a selected programmer knows only one of the two languages?
(d) If a programmer knows Java, what is the probability that he/she knows C/C++?
(e) If a programmer knows C/C++, what is the probability that he/she knows Java?
(f) Are the events “know Java” and “know C/C++” independent? Are then mutually exclusive? Explain.

Answer by ikleyn(52848)   (Show Source): You can put this solution on YOUR website!
.

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  employee knows both languages?
    (b) What is the probability that a selected  employee knows C/C++ but not Java?
    (c) What is the probability that a selected  employee knows only one of the two languages?


     The rest of questions (d), (e) and (f) are correct.


Solution

We are given  

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


Then   P(C ∩ 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 ∩ J) = 0.4.



(b)  This set is  C \ (C ∩ J);  therefore,

     this probability is equal to  P(C) - P(C ∩ J) = 0.7 - 0.4 = 0.3.



(c)  This probability is equal to  P(C U J) - P(C ∩ J) = 0.9 - 0.4 = 0.5.



(d)  This probability is  P(C ∩ J)/P(J) =  = .



(e)  This probability is  P(C ∩ J)/P(C) =  = .



(f)  To answer first part, compare  P(C)*P(J) with P(C ∩ J).

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


     To answer the second part,  compare  P(C ∩ J) with 0 (zero, ZERO).

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


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