Homework Answers
Using the fact we have,
P(successful product gets good review) = 0.95
P(unsuccessful product received good review) = 0.10
In addition for the new product designs,
P(products have been successful) = 0.40
P(products have been unsuccessful) = 0.60
a) P(product gets a good review) = [P(product has been successful) * P(successful product gets good reviews)] + [P(product has been unsuccessful) * P(unsuccessful product gets good reviews)]
Hence, P(product gets good review) = 0.40*0.95 + 0.60*0.10
= 0.38 + 0.06
= 0.44
Therefore, probability that the product gets good review is 0.44
b) The probability that we want to find out is,
P(There will be successful product given that new design gets a good review)
= P(product is successful and gets a good review) ÷ P(product gets a good review)
= [0.40*0.95] / 0.44 ..............(from (a))
= 0.38 / 0.44
= 0.8636
Hence, required probability is 0.8636
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