The freshman class of a private engineering college has 300 students. It is known that 180 can program in Java, 120 in Visual BASIC†, 30 in C++, 12 in Java and C++, 18 in Visual BASIC and C++, 12 in Java and Visual BASIC, and 6 in all three languages.
a) A student is selected at random. What is the probability that she can program in exactly two languages?
b) Two students are selected at random. What is the probability that they can
(i) both program in Java?
(ii) both program only in Java?
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