Question

An investor is considering a $25,000 investments in a startup company. She estimates that she has a probability 0.2 of a $15,000 loss, probability 0.05 of a $20,000 loss, probability 0.3 of a $35,000 profit, and probability 0.45 of breaking even ( a profit of $0). What is the expected value of the profit?

Answer 1

Given:

Total investments = $25000

She estimates the following:

Probability 0.2 of a $15,000 loss (-$15,000)

Probability 0.05 of a $20,000 loss (-$20000)

Probability 0.3 of a $35,000 profit (+35000)

Probability 0.45 of breaking even ($0)

Total probability = 0.2 + 0.05 + 0.3 + 0.45 = 1

Since the total probability is 1, to find the expected value of profit, we have:

$(-15000\times0.2)+(-20000\times0.05)+(35000\times0.3)+(0\times0.45)$

Solving further:

$\begin{gathered} (-3000)+(-1000)+(10500)+(0) \\ \\ =-3000-1000+10500 \\ \\ =6500 \end{gathered}$

Therefore, the expected value of the profit is $6,500

ANSWER:

a) $6,500