Adata scientist is building a model for a business to evaluate various metrics about the products and outlook. in looking at the data, she decides that a product should be continued if it sold 9500 over the previous year. in addition, the product is considered "popular" if it receives 200 mentions by the local press over the past year.

in selecting a product at random from the company’s web page, let c be the likelihood that this product reached the 9500 thresholds the past year. let p be the likelihood that the product received the 200 or more mentions by the local press.

the analyst determines that p(c) = 0.307, p(p) = 0.194, and the probability that a product has sold 9500 items, and was ‘popular’ is 0.084. what is the probability that a randomly selected product either sold the requisite 9500 items or that it is ‘popular’?

part b: where would the analyst have come up with the probability values for p(c) and p(p)?

any options?

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answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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