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Chapter 11: Problem 23

Describe a situation in which a business can use expected value.

Short Answer

Expert verified
A business planning to launch a new product can use expected value to predict the returns of the new product launch based on estimated probabilities and outcomes, and then compare that with the returns of sticking to their current product line. The decision is then made based on the comparison of the expected values.

Step by step solution

01

Identify the business situation

Select a situation where a business has to make a choice between different options. For example, a business wants to launch a new product, but they are unsure about how the product will perform in the market. They have two options, launch the new product or stick to their current product line.
02

Calculate the expected value

The business needs to estimate the probabilities and the potential outcomes (returns) for both scenarios. This could involve market research for gauging customer interests, studying trends, and estimating costs of production and marketing. Let's say the expected revenues are $90,000 with a probability of 0.1, $50,000 with a probability of 0.3 and $10,000 with a probability of 0.6 for launching the product, and a secure revenue of $30,000 if they stick to their current line. The expected value for the new product launch would be: \(E = (90,000*0.1) + (50,000*0.3) + (10,000*0.6) = 9,000 + 15,000 + 6,000 = $30,000\).
03

Make a decision

The decision would then be based on the expected value calculated. In this case, the expected value of the new product launch is the same as stick to their current line. This would mean that launching the new product might not be worth the risk as there is no expected monetary advantage.

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Most popular questions from this chapter

If a single die is rolled twice, find the probability of rolling an odd number and a number greater than 4 in either order.

Evaluate each factorial expression. \(\frac{106 !}{104 !}\)

Involve computing expected values in games of chance. A game is played using one die. If the die is rolled and shows 1 , the player wins \(\$ 1\); if 2 , the player wins \(\$ 2\); if 3 , the player wins \(\$ 3\). If the die shows 4,5 , or 6 , the player wins nothing. If there is a charge of \(\$ 1.25\) to play the game, what is the game's expected value? What does this value mean?

Involve computing expected values in games of chance. Another option in a roulette game (see Example 6 on page 753 ) is to bet \(\$ 1\) on red. (There are 18 red compartments, 18 black compartments, and 2 compartments that are neither red nor black.) If the ball lands on red, you get to keep the \(\$ 1\) that you paid to play the game and you are awarded \(\$ 1\). If the ball lands elsewhere, you are awarded nothing and the \(\$ 1\) that you bet is collected. Find the expected value for playing roulette if you bet \(\$ 1\) on red. Describe what this number means.

A coin is tossed and a die is rolled. Find the probability of getting a tail and a number less than 5 .
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