Questions: The table shows the result of a restaurant survey. Meals Service good Service poor Total Lunch 38 36 74 Dinner 14 45 59 Total 52 81 133 Find the probability the service was good, given that the meal was dinner. The probability the service was good, given that the meal was dinner, is (Type an integer or a simplified fraction.)

The table shows the result of a restaurant survey. Meals Service good Service poor Total Lunch 38 36 74 Dinner 14 45 59 Total 52 81 133 Find the probability the service was good, given that the meal was dinner. The probability the service was good, given that the meal was dinner, is (Type an integer or a simplified fraction.)
Transcript text: The table shows the result of a restaurant survey. \begin{tabular}{|c|c|c|c|} \hline Meals & Service good & Service poor & Total \\ \hline Lunch & 38 & 36 & 74 \\ Dinner & 14 & 45 & 59 \\ Total & 52 & 81 & 133 \\ \hline \end{tabular} Find the probability the service was good, given that the meal was dinner. The probability the service was good, given that the meal was dinner, is $\square$ (Type an integer or a simplified fraction.)
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Solution

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Solution Steps

Step 1: Understand the Problem

We are given a contingency table showing the results of a restaurant survey. We need to find the probability that the service was good, given that the meal was dinner. This is a conditional probability problem.

Step 2: Identify the Relevant Data

From the table, we have the following data for dinner:

  • Service good: 14
  • Total dinners: 59
Step 3: Calculate the Conditional Probability

The probability that the service was good, given that the meal was dinner, is calculated using the formula for conditional probability:

\[ P(\text{Service good} \mid \text{Dinner}) = \frac{\text{Number of good service dinners}}{\text{Total number of dinners}} \]

Substituting the values from the table:

\[ P(\text{Service good} \mid \text{Dinner}) = \frac{14}{59} \]

Final Answer

The probability that the service was good, given that the meal was dinner, is:

\[ \boxed{\frac{14}{59}} \]

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