(e) A and B are mutually exclusive Among employees of a certain firm, 70% know C

Question

(e) A and B are mutually exclusive Among employees of a certain firm, 70% know C/C++, 60% know Java, and 90% know at least one of th 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 Ja (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/Ct+? (e) If a programmer knows C/C++, what is the probability that he/she knows Java? (9) Are the events "know Java" and "know C/C++" independent? Are then mutually exclusive? Explain. ms for ai If this is ht. Ass Vhat is

Explanation / Answer

P(know C/C++) = 0.7

P(know java) = 0.6

a) P(at least one language) = P(know C/C++) + P(know java) - P(know both language)

or, 0.9 = 0.7 + 0.6 - P(know both language)

or, P(know both language) = 0.4

b) P(knows C/C++ but not java) = P(knows C/C++) - P(knows both language) = 0.7 - 0.4 = 0.3

c) P(knows only one language) = P(knows C/C++) + P(knows java) - 2 * P(knows both language) = 0.7 + 0.6 - 2 * 0.4 = 0.5

d) P(knows C/C++ | knows java) = P(knows C/C++ and knows java) / P(knows java) = 0.4 / 0.6 = 0.67

e) P(knows java | knows C/C++) = P(knows java and knows C/C++) / P(knows C/C++) = 0.4 / 0.7 = 0.5714

f) No, they are not mutuallly exclusive, because P(knows java and knows C/C++) is not equal to zero.

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