Question

Homework:

Give an example of a probability that informs a business decision.

Answer 1

Business Decisions

Jessica owns a manufacturing business, and she's considering adding another plant in a second state. The expansion could allow her company to produce more product and make more profit, but it's a gamble because it could also cost her company dearly. Should she do it?

Companies face decisions, both large and small, every day. There are many ways that business decisions can be made. One type of decision-making analysis involves using probabilities and economic measures to make decisions. To help Jessica make her decision, let's see how this type of analysis works.

Expected Value

Jessica is wondering how she should make her decision about opening a new plant. She thinks that crunching numbers will be better than just going with her gut or with what her company has always done, but there are so many possible outcomes: the new plant could make a ton of money, or it could tank and end up causing her company to go into bankruptcy. How can she figure out the best option?

One way to do that is to use the expected value of the different outcomes, which is the weighted payoff based on probabilities. For example, if Jessica believes that there's a 40% chance that the second plant will make a profit of $100,000 in its first year, then the expected value of that plant is $100,000 x .4, or $40,000.

But, let's say that there's also a 30% chance that the second plant will only make $10,000 in that first year. That expected value is $3,000. And if there's a 20% chance that the plant will lose $100,000 in the first year, then the expected value is -$20,000.

So, which option should Jessica go with when trying to make her decision? One thing Jessica can do is to add up the different options. $40,000 + $3,000 + -$20,000 = $23,000. That's the total expected value of what might happen in the first year of the plant's opening.

How does Jessica figure out the probability of different outcomes? There are two ways to calculate expected value. The first is to calculate it based on objective probability, or using actual data to figure out probability. For example, if Jessica has data that shows that similar manufacturing plants made $100,000 profit in their first year about 40% of the time, that's objective probability; she's using actual data to figure out the probability of her plant making $100,000 profit in the first year.

But, what if she doesn't have data to use? The other way to calculate the expected value is with subjective probability, or using a rough estimate to figure out probability. If Jessica doesn't have data (or if she has only scant data), she can make a 'guestimate' about what she thinks the probability of each outcome is.