Question

A company creates a new snack, \(\mathrm{N}\), and tests it against its current leader, L. The table shows the results. $$ \begin{array}{|l|c|c|} \hline & \text { Prefer L } & \text { Prefer N } \\ \hline \text { Current L Consumer } & 72 & 46 \\ \hline \text { Not Current L Consumer } & 52 & 114 \\ \hline \end{array} $$ The company is deciding whether it should try to improve the snack before marketing it, and to whom the snack should be marketed. Use probability to explain the decisions the company should make when the total size of the snack's market is expected to (a) change very little, and (b) expand very rapidly.

Short answer

In a stable market (Scenario A), focus should be on the current L consumers - if a considerable portion of them prefer N, market as it is, else consider improvements. In an expanding market (Scenario B), the focus should expand to non L consumers. If a substantial portion of them prefer N, aggressive marketing can be employed.

Step-by-step solution

Calculate Total Number of Consumers

Firstly, add all the values given in the table to find out the total number of consumers. This will be useful for calculating probabilities. So, Total consumers = 72 (Current L consumers preferring L) + 46 (Current L consumers preferring N) + 52 (Non L consumers preferring L) + 114 (Non L consumers preferring N)

Calculate Conditional Probabilities

For a market that isn't expanding quickly, interest will primarily be in current consumers. The probability of a current L consumer preferring snack N is calculated by dividing the number of current L consumers who prefer N (46) by the total number of current L consumers (72 + 46). Do a similar calculation for Non L consumers.

Market Analysis for Scenario A

Use the calculated probabilities to decide where to focus marketing efforts. If the probability of current L consumers preferring N is large, it may be worth it to market towards them. Otherwise, improvements might be required based on the probability.

Market Analysis for Scenario B

In a rapidly expanding market, new consumers will also need to be considered. If the probability of non L consumers preferring N is large, it may be wise to market towards them, even if that means slight disfavor among current L consumers.

Key concepts

Conditional Probability in Marketing Decisions

Understanding conditional probability is crucial when making informed marketing decisions. This concept deals with evaluating the likelihood of an event occurring, given that another event has already happened. For the company in question, knowing how current consumers of product L respond to the new snack N is essential.

In practice, if we let A represent the event that a consumer prefers snack N, and B represent the event that the consumer is currently an L consumer, then the conditional probability of A given B is calculated by dividing the number of L consumers who prefer N by the total number of L consumers. Mathematically, it is expressed as: \[ P(A|B) = \frac{\text{Number of L consumers preferring N}}{\text{Total number of L consumers}} \].

This insight tells the company how likely they are to convince their existing customers to switch to the new product. If the ratio is high, the company might focus its efforts on the existing customer base; if it's low, they might consider product improvement or target different groups.

Market Analysis

Market analysis is vital for assessing the potential success of a new product and formulating the right strategies. The example given requires analyzing the preference statistics and deciding whether to improve the product based on those insights.

For scenario A, where the market size changes little, the focus is on current consumers, making their preferences paramount. The company should assess if there's enough favorability towards snack N. They might not need to revamp their product if existing customers show a significant preference for it over their current offering, snack L.

In contrast, scenario B involves a rapidly expanding market. Here, it's important to consider not only current L consumers' preferences but also those of potential new consumers. These are individuals who don't currently consume snack L but may prefer snack N. The company must analyze this segment because winning them over can contribute to significant market share gains as the market grows.

Consumer Preference Statistics

Consumer preference statistics give actionable insights into customer choices and behaviors. In the situation of the snack company, the statistics can guide which segment to target and whether the new snack needs improvements.

The table of results serves as raw data for understanding customer preferences. For instance, one can calculate the percentage of current L consumers who might prefer the new snack N. Likewise, the data also reveals the acceptance rate among non-L consumers, which potentially represents the larger portion of an expanding market.

It is critical to translate these statistics into a clear picture of consumer satisfaction. If a significant percentage of current L consumers prefer the new snack, marketing efforts could potentially shift to capitalizing on brand loyalty. However, if the adoption rate is higher among non-L consumers in a growing market, it would be strategic to attract those consumers instead, balancing efforts to retain current customers without neglecting potential new ones.