UCD administrators are interested in the relationship between a student’s score
on a first year maths module and their final grade classification. From a sample of
725 students who completed their degree, 612 obtained a C or above on the maths
module in their first year, and 376 of the 725 ended up with a 2:1 degree or above.
335 of the 725 both got a C or above in the module and ended up with a 2:1 or
above degree. Let A be the event that a student gains a C or above on the maths
module, and B the event that a student ends up with a 2:1 or above for their final
degree.
(a) What are the names of the two main interpretations of probability? Briefly
explain how they differ.
[3 marks]
(b) Given the data above, calculate:
(i) P(A \cap B)
[1 mark]
(ii) P(A \cup B)
[2 marks]
(c) Define the terms ‘independent’, ‘mutually exclusive’, and ‘exhaustive’. Do any
of these terms apply to events A and B? Explain your answers.
[4 marks]
(d) What is the probability that a student will gain a 2:1 or above given that they
obtain C or above in the maths module? What is the probability that they will
get a 2:1 or above given that they do not obtain a C or above? Interpret your
answer