Customers are used to evaluate preliminary product design. In the past, 90% of h
ID: 3179134 • Letter: C
Question
Customers are used to evaluate preliminary product design. In the past, 90% of highly successful products received good reviews, 50% of moderately successful products received good reviews, 10% of poor products received good reviews. In addition, 60% of products have been highly successful, 30% of products have been moderately successful, and 10% of products have been highly successful. (a) What is the probability that a product receives good review and is highly successful? P(G H) = 1.5 times 0.6 = 0.9 (b) If a product receives good review, what is the probability that it will highly successful? (c) If a product doesn't receive good review, what is the probability that it will be highly successful? (d) What is the probability that a product receives good review? P(G) = 0.9+0.5+0.1 = 1.5 (e) Is the event receiving good review is independent from the event becoming highly successful product? P(B|A) = P(A) P(A|B) = P(B) P(A B) = P(A) middot P(B)Explanation / Answer
(b) now we want to find
P( highly successful / good review ) =?
By using the bayes Rule
=P ( highly sucessful ) P ( good review / highly successful ) / { P(highly succesful ) * P( good review / highly successful) + P( Moderately successful ) P( good review / moderately successful ) + P( poor product ) P( goodreview / poor product )
= 0.60 * (0.90) / {( 0.60 * (0.90)) + (0.30*(0.30))+(0.10 *(0.10)
= 0.54 / 0.64
= 0.84375
(c)
now we want to find
P( highly successful / bad review ) =?
By using the bayes Rule
=P ( highly sucessful ) P ( bad review / highly successful ) / { P(highly succesful ) * P( bad review / highly successful) + P( Moderately successful ) P( bad review / moderately successful ) + P( poor product ) P( bad review / poor product )
= 0.60 * (1-0.90) / {( 0.60 * (1-0.90)) + (0.30*(1-0.30))+(0.10 *(1-0.10)
=0.06 / 0.36
= 0.1667
(d)
P ( Probablity that product received good review ) =?
= 0.90*0.50 * 0.10
=0.045
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