Question #16654

A business man has 2 independent investment A and B available to him, but he llacks the capital to undertake both of them simultaneously. He can choose to take A first and then stop, of if A is unsucsessful then take B or vice versa. The probability of success on A is 0.7 while for B it is 0.4. Both investments rquire an initial capital outlay of R2000 and both return nothing if the venture is unsucessful. Sucessful completion of A will return R3000 (over cost), while sucessful completion of B will return R5000 (over cost)
How would I prepare a report with the aid of a decision tree, advising the investor of the best course of action?

Expert's answer

If the investor chooses to invest first in A, then he pays 2000 for such possibility with probability 0.7 he earns 5000 or A is unsuccessful (the probability 0.3 ), takes B, pays 2000 for such action and the probability 0.4 earns 7000 or earns nothing, the expected value of such strategy is −2000+0.7·5000+0.3(−2000+0.4·7000) = 1.740.

If the investor chooses to invest first in B, then he also pays 2000 for such a possibility, with probability 0.4 gains 7000 or with probability 0.6 B is unsuccessful and so then he takes A, pays for such possibility 2000 and with probability 0.7 it gives him 5000 or with probability 03 nothing.

The expected value of such strategy is 0.4 · 7000 − 2000 + 0.6(−2000 + 0.7 · 5000) = 1700. To conclude, the 1 strategy is better.

Answer. The first strategy is better

If the investor chooses to invest first in B, then he also pays 2000 for such a possibility, with probability 0.4 gains 7000 or with probability 0.6 B is unsuccessful and so then he takes A, pays for such possibility 2000 and with probability 0.7 it gives him 5000 or with probability 03 nothing.

The expected value of such strategy is 0.4 · 7000 − 2000 + 0.6(−2000 + 0.7 · 5000) = 1700. To conclude, the 1 strategy is better.

Answer. The first strategy is better

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