Question

An investment counselor calls with a hot stock tip. he believes that if the economy remains​ strong, the investment will result in a profit of ​$50 comma 000. if the economy grows at a moderate​ pace, the investment will result in a profit of ​$10 comma 000. ​however, if the economy goes into​ recession, the investment will result in a loss of ​$50 comma 000. you contact an economist who believes there is a 30​% probability the economy will remain​ strong, a 60​% probability the economy will grow at a moderate​ pace, and a 10​% probability the economy will slip into recession. what is the expected profit from this​ investment?

Answer 1

Answer: $ 16,000 profit

Step-by-step explanation:

Given the following :

Profit when economy is strong = 50,000

Profit when economy is moderate = 10,000

Loss when economy goes into recession = 50000

Resulting probabilities of the three probable occurrences are:

Probability of strong economy; p(strong) = 30/100 = 0.3

Probability of moderate; P(moderate) = 60/100 = 0.6

Probability of recession; P(recession) = 10/100 = 0.1

Expected profit :

Summation of the product of each probability and its accompanying profit or loss.

P(strong) × profit of strong = 0.3 × 50000 = 15000

P(moderate) × profit of moderate = 0.6 × 10000 = 6000

P(recession) × loss on recession = 0.1 × 50000 = 5000 = - 5000 ( loss)

Expected profit :

$(15,000 + 6000 - 5000) = $16,000 profit