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: (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; (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?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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:
(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;
(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
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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