Question P20: An investment company, ABI, determines from its market share that
ID: 3368878 • Letter: Q
Question
Question P20: An investment company, ABI, determines from its market share that 10% of investors choose ABI to -manage their portfolios. A recent industry survey reveals that 20% of people invest in mining, given they choose ABI to manage this portfolio. The survey revealed that only 5% of people invest in mining, given they used an alternative firm to manage their portfolio. To assess the potential attraction of people to ABI because of its successful portfolio management in mining investments, wishes to determine the likelihood a person will choose ABI Investments, given they have chosen to invest in mining. You determine this probability to be the firm (a) (b) 2% 4.5% (d) 69.23%Explanation / Answer
Solution
Let A represent the event that investors choose ABI to manage their portfolio and B represent the event that investor invests in mining.
With the above terminology, the given data translates as follows:
P(A) = 0.1 ……………………………………………………………………. (1) and hence
P(AC) = 0.9 ……………………………………………………………………. (2)
P(B/A) = 0.2 ……………………………………………………………………. (3)
P(B/AC) = 0.05 ……………………………………………………………………. (4)
Back-up Theory
If A and B are two events such that probability of B is influenced by occurrence or otherwise of A, then
Conditional Probability of B given A, denoted by P(B/A) = P(B ? A)/P(A)..….(1)
P(B) = {P(B/A) x P(A)} + {P(B/AC) x P(AC)}………………………………….(2)
P(A/B) = P(B/A) x {P(A)/P(B)}……………………………..………………….(3)
Now, to work out the solution,
We want the likely-hood that investors would choose ABI given that they invest in mining.
i.e., P(A/B).
Vide (3), P(A/B) = (0.2 x 0.1)/P(B) …………………………………………… (4)
Again, Vide (2), P(B) = (0.2 x 0.1) + (0.05 x 0.8)
= 0.06 …………………………………………………………………………..(5)
(4) and (5): P(A/B) = (0.2 x 0.1)/0.06
= 1/3 = 0.3333 ANSWER
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