Draw a probability tree to help you to work out the probability that a randomly chosen person is willing to pay for a more expensive shoe design; and the probability that a person has a knee concern given they are willing to pay for a more expensive shoe design? (round your answers to 4dp.)
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.
Mary and her colleague have collected information from the same sample on their willingness to pay for a more expensive shoe design which helps to reduce the impact on the knees while running. In the sample they have collected, there are 200 people that own at least one pair of running shoes. 20% of the running shoes’ owners have some concerns about their knees, and 50% of those with knee concerns are willing to pay for a more expensive shoe design. The other 80% don’t have this concern, and only 20% of those without knee concerns are willing to pay for a more expensive shoe design.
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