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.