Question

Claire is considering investing in a new business. In the first year, there is a probability of 0.2 that the new business will loose $10,000, a probability of 0.4 that the new business will break even ($0 loss or gain), a probability of 0.3 that the new business will make $5,000 in profits, and a probability of 0.1 that the new business will make $8,000 in profits.

A. Claire should invest in the company if she makes a profit. Should she invest? Explain using expected values.

B. If Claire’s initial investment is $1,200 and the expected value for the new business stays constant, how many years will it take for her to earn back her initial investment?

Answer 1

(a)Yes, she would make a profit of $300

(b)4 years

Explanation:

The probability distribution table of Claire's profit is presented below.

`\left|\begin{array}c$Profit, x&-\$10000&\$0&\$5000&\$8000\\P(x)&0.2&0.4&0.3&0.1\end{array}\right|`

(a)Expected Profit = (-10000 X 0.2)+(0 x 0.4)+(5000 X 0.3)+ (8000 X 0.1)

=$300

Claire should invest in the company as she is expected to make a profit of $300.

(b)If Claire’s initial investment is $1,200 and the expected value for the new business stays constant

$1200/$300=4

Therefore, it will take her 4 years to earn back her initial investment.