a) Calculate the probability that a customer who tested the blue packet will buy the cereal. (b) The probability that a consumer who tested the green packet will not or will likely not buy the cereal (c) Calculate the probability that a randomly selected customer who indicated he will buy the cereal tested the yellow packet;
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.
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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.
A market research company is conducting a study on the packaging of a new breakfast cereal, which one of its clients is about to launch. Four different colours were used as the main colour in the packaging and customers were asked whether they were likely to try the new cereal. 500 people participated in the study and their replies are summarised in the table:
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(a) Calculate the probability that a customer who tested the blue packet will buy the cereal.
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(b) The probability that a consumer who tested the green packet will not or will likely not buy the cereal
(c) Calculate the probability that a randomly selected customer who indicated he will buy the cereal tested the yellow packet;
(d) Whether the probability that a customer “Likely Will” buy the cereal is independent of the colour of the packet. Show the calculations to support your answer.
(e) Provide the definition of mutually exclusive and collectively exhaustive for two events.
(f) Any selected events from Packet colour categories and Buying intention categories (select one
event from Packet colour and one event from Buying intention) are mutually exclusive? Why?(g) Calculate the odds for a Yellow Packet colour and a Likely will not Buying intention separately. Are these two events collectively exhaustive? Why?
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