• 5 Marks

QT – Nov 2016 – L1 – Q1c – Probability

This question deals with calculating the conditional probability of earning more than GHC 5,000 given that an ICAG-qualified individual stays at a university.

If selected by the panel, the probability that an ICAG-qualified member will remain with the Private University is 0.6, and the probability that a Chartered Accountant earns more than GHC 5,000 per month in the university is 0.5. If the probability that Mr. Agbagba will remain with the university or earn more than GHC 5,000 per month is 0.7:

Required:
Calculate the probability that he will earn more than GHC 5,000 per month given that he is a Chartered Accountant who will stay with the university.

Let ICAG be the event a Chartered Accountant stays with the university, and let GHC 5000 be the event of earning more than GHC 5,000 per month.

P (ICAG ∪ GHC5000) = P (ICAG)+P (GHC5000) − P (ICAG ∩ GHC5000)

0.7 = 0.6 + 0.5 − P (ICAG ∩ GHC5000)

P (ICAG ∩ GHC5000) = 1.1 − 0.7 = 0.4

The probability of earning more than GHC 5,000 given that he stays with the university is:

P (GHC5000 ICAG) =

 

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