(Scenario: Buying Shares)Use Scenario: Buying Shares.The probability that Geordie will sustain a loss is _____% if he invests $1,000 in either Apple or Microsoft and _____% if he invests $500 apiece in Apple and in Microsoft. Scenario: Buying Shares
Geordie is considering buying shares in two companies,Apple and Microsoft.If he invests $1,000 in Apple,there is a 40% probability that his investment will be worth only $800 and a 60% probability that it will be worth $1,200 at the end of a year.If he invests $500 in Apple,there is a 40% probability that his investment will be worth $400 and a 60% probability that it will be worth $600 at the end of a year.The corresponding numbers for investment in Microsoft are identical.
A)40;40
B)40;16
C)80;20
D)40;80

Question

Quizplus · Accepted Answer

If Geordie invests $1,000 in either Apple or Microsoft, the possible outcomes and their respective probabilities are:

- $800 (40% probability)
- $1,200 (60% probability)

Therefore, the expected value of his investment would be:

(0.4 x $800) + (0.6 x $1,200) = $1,040

There is a 60% chance that he would make a profit, but there is still a 40% chance that he would sustain a loss.

However, if Geordie invests $500 in both Apple and Microsoft, the possible outcomes and their respective probabilities are:

- $400 (16% probability) [0.4 x 0.4]
- $1,000 (48% probability) [0.6 x 0.4 + 0.4 x 0.6]
- $1,200 (36% probability) [0.6 x 0.6]

Therefore, the expected value of his investment would be:

(0.16 x $400) + (0.48 x $1,000) + (0.36 x $1,200) = $1,080

There is a lower probability of sustaining a loss (16%), and the expected value of his investment is higher ($1,080 compared to $1,040 if he invests $1,000 in one company). Therefore, the best choice is to invest $500 in both Apple and Microsoft.