Probability: Relationship between two consumables

A simple random sample of 227 university students were asked what pasta they
usually order and with which sauce. The preferences of these respondents are
summarised below:
(a) Use Excel to obtain a 100% stacked column chart for the data from the table. What
does your chart suggest between the relationship between Pasta and Sauce?
(4 Marks)
EXCEL Instructions: Refer to Topic 6 in the Excel Booklet for instructions on how
to obtain 100% stacked column chart.

(b) Use the contingency table to calculate the following probabilities; include an
appropriate probability statement for each case:
i. What is the probability that a respondent prefers Gnocchi?
(2 Marks)
ii. What is the probability that a respondent prefers Spaghetti and Bolognese
sauce?
(3 Marks)
iii. What is the probability that a respondent prefers Ravioli or Carbonara
sauce?
(3 Marks)
iv. Suppose the preferred sauce is Pesto. What then is the probability the pasta
ordered is Ravioli?
(3 Marks)
v. Suppose that the preferred Pasta is Spaghetti. What then is the probability
the sauce ordered is Bolognese?
(3 Marks)
(c) Are the events Gnocchi and Sauce statistically independent or dependent? How
do you know? Show all calculations that support your answer.
(7 Marks)
(Total for 25 Marks)

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