Question

At a particular restaurant, % of all customers order an appetizer and % of all customers order dessert. If % of all customers order an appetizer or dessert (or both), what is the probability a randomly selected customer orders both an appetizer and dessert?

Answer 1

Answer on Question #58369 – Math – Statistics and Probability Question

At a particular restaurant, % of all customers order an appetizer and % of all customers order dessert. If % of all customers order an appetizer or dessert (or both), what is the probability a randomly selected customer orders both an appetizer and dessert?

Solution

At a particular restaurant, $x\%$ of all customers order an appetizer and $y\%$ of all customers order dessert. If $z\%$ of all customers order an appetizer or dessert (or both), then the probability a randomly selected customer orders both an appetizer and dessert is as follows:

$$P(\text{Appetizer} \cap \text{Dessert}) = P(\text{Appetizer}) + P(\text{Dessert}) - P(\text{Appetizer} \cup \text{Dessert}) = \frac{x}{100} + \frac{y}{100} - \frac{z}{100}.$$

Answer: $\frac{x}{100} + \frac{y}{100} - \frac{z}{100}$.

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