Question 11 An investment company, ABI, determines from its market share that 10

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Question 11 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, the firm 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: A. 2% B. 4.5% C. 30.77% D. 69.23% E. None of the above is correct Question 12 Brett, a small business owner of Drywall Plumbing has been told that his investment funds will take between 5 and 10 days to transfer to his day-to-day account. He has a bill due in 7 days. What is the probability that the funds will be available in time to pay the bill? A. 30% B. 40% C. 60% D. 70% E. 80%

Explanation / Answer

Q.11

An investment company, ABI, determines from its market share that 10% of investors choose ABI to manage their portfolios.

                                                     P(A) = 0.10

A recent industry survey reveals that 20% of people invest in mining, given they choose ABI to manage this portfolio.

                                                  P(M | A) = 0.20

The survey revealed that only 5% of people invest in mining, given they used an alternative firm to manage their portfolio.

                                                 P(M | Ac) =0 .05

We have to find

P(A | M) = ?

From Bayes theorem

P(A | M) = P(A).P(M|A) / [ P(A).P(M|A) + P(Ac ).P(M | Ac ) ]

= (0.1)(0.2) / [(0.1)(0.2) + (0.9)(0.05) ] = .02 / (.02 + .045) =0 .307692

So, I believe 'C' should be the answer.

Q. 12

Since, no information about the distribution is given, we will assume it to be uniform.

a = 5; b=10;

Height of uniform distribution = 1 / (b-a) = 1 / (10-5) = 1/5 =0 .2

P(x<=7) = (7-5)*.2 = 2*.2 = .4     {This is the area of rectangle from 5 to 7 having height of 0.2}

Thus, 'B' will be the answer.

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