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A software company surveyed managers to determine the probability that they would buy a new graphics package that includes three-dimensional graphics

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A software company surveyed managers to determine the probability that they would buy a new graphics package that includes three-dimensional graphics. About 20% of office managers were certain that they would not buy the package, 70% claimed that they would buy, and the others were undecided. Of those who said that they would not buy the package, only 10% said that they were interested in upgrading their computer hardware. Of those interested in buying the graphics package, 40% were also interested in upgrading their computer hardware. Of the undecided, 20% were interested in upgrading their computer hardware.

Let A denote the intention of not buying, B the intention of buying, C the undecided, and G the intention of upgrading the computer hardware.

(a) Calculate the probability that a manager chosen at random will not upgrade the computer hardware (P(G)).

(b) Explain what is meant by the posterior probability of B given G, P(B|G).

(c) Construct a tree diagram and use it to calculate the following probabilities: P(G), P(B|G), P(B|G), P(C|G), P(C|G).