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A consumer products company found that ​% of successful products also received favorable results from test market​ research, whereas ​% had unfavorable results but nevertheless were successful. That​ is, P(successful product and favorable test ​market) and​ P(successful product and unfavorable test ​market). They also found that ​% of unsuccessful products had unfavorable research​ results, whereas ​% of them had favorable research​ results, that is​ P(unsuccessful product and unfavorable test ​market) and​ P(unsuccessful product and favorable test ​market). Find the probabilities of successful and unsuccessful products given known test market​ results, that​ is, P(successful product given favorable test​ market), P(successful product given unfavorable test​ market), P(unsuccessful product given favorable test​ market), and​ P(unsuccessful product given unfavorable test​ market).

User Crhodes
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Answer:

P(successful product given favorable test​ market) = 77.19%

P(successful product given unfavorable test​ market) = 22.81%

P(unsuccessful product given favorable test​ market) = 25.58%

P(unsuccessful product given unfavorable test​ market) = 74.42%

Step-by-step explanation:

the information is incomplete since it is missing the numbers:

"A consumer products company found that 44​% of successful products also received favorable results from test market​ research, whereas 13​% had unfavorable results but nevertheless were successful. That​ is, P(successful product and favorable test ​market) = 0.44 and​ P(successful product and unfavorable test ​market) = 0.13. They also found that 32​% of unsuccessful products had unfavorable research​ results, whereas 11​% of them had favorable research​ results, that is​ P(unsuccessful product and unfavorable test ​market) = 0.32 and​ P(unsuccessful product and favorable test ​market) = 0.11."

probability of being successful and having favorable test market results = 44%

probability of being successful and having unfavorable test market results = 13%

probability of not being successful and having unfavorable test market results = 32%

probability of not being successful and having favorable test market results = 11%

probability of being successful = 44% + 13% = 57%

probability of not being successful = 32% + 11% = 43%

probability of being successful given favorable test​ market = 44% / 57% = 0.7719 = 77.19%

probability of being successful given unfavorable test​ market = 13% / 57% = 0.22819 = 22.81%

probability of not being successful given favorable test​ market = 11% / 43% = 0.2558 = 25.58%

probability of not being successful given unfavorable test​ market = 32% / 43% = 0.7442 = 74.42%

User BValluri
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