Work It Out, Chapter 20, Step 1

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
In this problem, you were asked to evaluate the expected payoff to purchasing a stock in General Motors under three different outcomes. You were considering spending 1 thousand dollars on General Motors stock and have a 0.4 probability of earning 1 thousand 600 dollars, 0.4 probability of earning 1 thousand 100 dollars, but a 0.2 probability of earning 800 dollars.

(Description)
The following text is written: You have 1000 dollars that you can invest. If you buy General Motors stock, then, in one year’s time: with a probability of 0.4 you will get 1 thousand 600 dollars; with a probability of 0.4 you will get 1 thousand 100 dollars; and with a probability of 0.2 you will get 800 dollars. If you put the money into the bank, in one year’s time you will get 1 thousand 100 dollars for certain. a. What is the expected value of your earning from investing in General Motors stock?

(Speaker)
We start by calculating the weighted average of the ending stock price, first, by multiplying 0.4 by 1 thousand 600 dollars.

(Description)
The following expression is written below the previous text: Left-parenthesis 0.4 times 1600 dollars right-parenthesis.

(Speaker)
Next we add the expected payout of 1 thousand 100 dollars, which is found by multiplying 0.4 times 1 thousand 100 dollars.

(Description)
The following expression is added to the previous one: Plus left-parenthesis 0.4 times 1100 dollars right-parenthesis.

(Speaker)
Next we need to add in the expected payout of 800 dollars, which is found by multiplying 0.2 times 800 dollars.

(Description)
The following expression is added to the previous one: Plus left-parenthesis 0.2 times 800 dollars right-parenthesis.

(Speaker)
Finally, we need to subtract the original purchase of 1 thousand dollars.

(Description)
The following expression is added to the previous one: Minus 1000 dollars.

(Speaker)
We are going to reduce the expression.

(Description)
The following expression is added to the previous one and written in the next row: equals 640 dollars plus 440 dollars plus 160 dollars minus 1000 dollars.

(Speaker)
You'll notice that because the change of ending up with a bad outcome is only 20 percent and the size of the loss is not large, the expected payout is going to be greater than zero dollars. Adding up everything, we have an expected payoff of 240 dollars.

(Description)
The following expression is added to the previous one: equals 240 dollars.