Explanation Given: The probability that the new product will be successful is 0.5 and the probability that it will be unsuccessful is 0.5. Explanation: Consider a new product introduced by a company. The probability that the new product will be successful is 0.5 and the probability that it will be unsuccessful is 0.5. If S represents the event that the product is successful and U represents the event that the product is unsuccessful, then P ( S ) = 0.5 and P ( U ) = 0.5 Successful products pass quality control 80% of the time and unsuccessful products pass quality control 25% of the time. If P represents the event that the product passes quality control, then P ( P S ) = 0.80 and P ( P U ) = 0.25 Use the Bayes’ Theorem P ( F E ) = P ( F ) × P ( E F ) P ( F ) × P ( E F ) + P ( F ' ) × P ( E F ' ) . The probability that the product is successful, if it passes quality control is P ( S P ) = P ( S ) × P ( P S ) P ( S ) × P ( P S ) + P ( U ) × P ( P S ) = 0.5 × 0.80 0.5 × 0.80 + 0.5 × 0.25 = 0.40 0.40 + 0

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 8, Problem 65RE

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The expected net profit of a company after the introduction of a new product.

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Chapter 8, Problem 64RE

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The expected net profit of a company after the introduction of a new product.

Solution Summary: The author analyzes the probability that a new product will be successful and unsuccessful. Successful products pass quality control 80% of the time.

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