SOLUTION: Oasis is an asset management company in South Africa. It has found that there is a three-in-five chance that a general equity unit trust fund will perform better than the overall J

Question 1145295: Oasis is an asset management company in South Africa. It has found that there is a three-in-five chance that a general equity unit trust fund will perform better than the overall JSE share index over any one-year period. If seven general equity unit trust funds are randomly selected from general equity unit trust funds.
2.1) What is the probability that all of these general equity unit trust funds performed better than the overall JSE share index over the past year (rounded off to three decimals)? [2]
2.2) What is the probability that at most two of these general equity trust funds performed better than the overall JSE share index over the past year (rounded off to three decimals)? [3.5]
2.3) What is the probability that more than two but less than five performed worse than the overall JSE share index over the past year (rounded off to three decimals)? [3.5]
2.4) For 150 general equity unit trust funds, what is the expected number of general equity unit trust funds that will perform better than the overall JSE share index (rounded off to zero decimals)?

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Let's take care of 2.4 first:

ANSWER: (3/5) of 150 = 90

For 2.1 through 2.3, the calculations are straightforward; you won't learn anything by having us do them for you. What you need is the probabilities that certain numbers of trust funds will perform better than the JSE average.

(1) Calculate the probabilities for 0, 1, 2, ..., 7 of the seven selected funds doing better than the average.
(2) To check your calculations, verify that the sum of those probabilities is equal to 1.
(3) Combine the individual probabilities as appropriate to answer 2.1 through 2.3.

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