A consumer products company found that 46% of successful products also received favorable results from test market research, whereas 14% had unfavorable results but nevertheless were successful. That is, P(successful product and favorable test market) = 0.46 and P(successful product and unfavorable test market) = 0.14.. They also found that 29% of unsuccessful products had unfavorable research results, whereas 11% of them had favorable research results, that is P(unsuccessful product and unfavorable test market) =0.29 and P(unsuccessful product and favorable test market) = 0.11. 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). P(successful product given favorable test market) = (Round to two decimal places as needed.)

A consumer products company found that 46% of successful products also received favorable results from test market research, whereas 14% had unfavorable results but nevertheless were successful. That is, P(successful product and favorable test market) = 0.46 and P(successful product and unfavorable test market) = 0.14.. They also found that 29% of unsuccessful products had unfavorable research results, whereas 11% of them had favorable research results, that is P(unsuccessful product and unfavorable test market) =0.29 and P(unsuccessful product and favorable test market) = 0.11. 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). P(successful product given favorable test market) = (Round to two decimal places as needed.)

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 14CR

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Concept explainers

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.

Question

A consumer products company found that 46% of successful products also received favorable results from test market research, whereas 14% had unfavorable results
but nevertheless were successful. That is, P(successful product and favorable test market) = 0.46 and P(successful product and unfavorable test market) = 0.14. They
also found that 29% of unsuccessful products had unfavorable research results, whereas 11% of them had favorable research results, that is P(unsuccessful product
and unfavorable test market) =0.29 and P(unsuccessful product and favorable test market) = 0.11. 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).
P(successful product given favorable test market) =
(Round to two decimal places as needed.)
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