A question on the mind of every statistics lecturer is, quite naturally, "What is the preferred Shapes flavour of my students?" So a stats lecturer surveyed their students, asking them their flavour preference (and, out of interest, their handedness).Use the cross table you generated for Computer Lab Week 2 to answer the following questions (round to 3 decimal places, where relevant):

a.   What is the probability that a randomly selected student is left handed?

[Fill in the blank],
Round your answer to 3 decimal places

b.   What is the probability that a randomly selected student prefers pizza Shapes?

[Fill in the blank],
Round your answer to 3 decimal places

c.   What is the probability that a randomly selected student is left handed AND prefers pizza Shapes?

[Fill in the blank],
Round your answer to 3 decimal places

d.   What is the probability that a randomly selected student is left handed, given that the student prefers pizza Shapes?

[Fill in the blank],
Round your answer to 3 decimal places

e.   What is the probability that a randomly selected student prefers pizza Shapes, given that the student is left handed?

[Fill in the blank],
Round your answer to 3 decimal places

Question

A question on the mind of every statistics lecturer is, quite naturally, "What is the preferred Shapes flavour of my students?" So a stats lecturer surveyed their students, asking them their flavour preference (and, out of interest, their handedness).Use the cross table you generated for Computer Lab Week 2 to answer the following questions (round to 3 decimal places, where relevant):

a.   What is the probability that a randomly selected student is left handed?­­­­­­

[Fill in the blank],
  Round your answer to 3 decimal places

b.   What is the probability that a randomly selected student prefers pizza Shapes?

[Fill in the blank],
  Round your answer to 3 decimal places

­­­c.   What is the probability that a randomly selected student is left handed AND prefers pizza Shapes?

[Fill in the blank],
  Round your answer to 3 decimal places

d.   What is the probability that a randomly selected student is left handed, given that the student prefers pizza Shapes?

[Fill in the blank],
  Round your answer to 3 decimal places

e.   What is the probability that a randomly selected student prefers pizza Shapes, given that the student is left handed?

[Fill in the blank],
  Round your answer to 3 decimal places

BlackTom AI · Accepted Answer

This item asks you to compute several probabilities from a cross table of handedness (left-handed vs not left-handed) and pizza Shapes flavour preference. However, the actual cross tabulated counts are not provided in the prompt, so we cannot compute numeric values yet.

First, identify what data you need from the cross table:
- Total number of students (the grand total).
- The marginal total for left-handed students (to answer parts a and c and d).
- The marginal total for students who prefer pizza Shapes (to answer parts b and d and e).
- The joint counts for left-handed students who prefer pizza Shapes (for part c).
- The conditional counts required by parts d and e, which rely on the joint and marginal totals.

Next, outline the formulas you would apply once you have the counts:
- a) P(left-handed) = (number of left-handed students) / (total number of students).
- b) P(prefers pizza Shapes) = (number who prefer pizza Shapes) / (total number of students).
- c) P(left-handed AND prefers pizza Shapes) = (joint count) / (total number of students).
- d) P(left-handed | prefers pizza Shapes) = P(left-handed AND prefers pizza Shapes) / P(prefers pizza Shapes) = (joint count) / (number who prefer pizza Shapes).
- e) P(prefers pizza Shapes | left-handed) = P(left-handed AND prefers pizza Shapes) / P(left-handed) = (joint count) / (number of left-handed students).

To proceed, locate the cross table you generated for Computer Lab Week 2 and extract the following values:
- N = total observations.
- N_left = total left-handed individuals.
- N_pizza = total individuals who prefer pizza Shapes.
- N_left_pizza = number who are left-handed and prefer pizza Shapes.

With these four numbers, you can fill in all blanks in parts a–e using the formulas above. If any part yields a division by zero (for example, if there are no left-handed students or no pizza-preferring students), you would report that the probability is undefined for that conditional calculation and explain why.

If the cross table is organized with rows as handedness (Left, Not Left) and columns as Shape flavour (Pizza Shapes, etc.), ensure you read the margins correctly and avoid mixing up row versus column totals when computing conditional probabilities.

Finally, when you fill in the blanks to three decimal places, apply standard rounding rules: look at the fourth decimal place to decide whether to round up or down.

In the absence of the actual frequency data, the steps above show exactly how to compute each requested probability once the cross table counts are provided. If you share the specific counts from the cross table, I can execute the calculations and present the numeric answers rounded to three decimals for parts a through e.

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