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Use numerals instead of words. For answers that are not whole numbers, round to the thousandths place.

Management at a restaurant is deciding whether to add a new Italian or Chinese dish to their menu. They randomly select customers to survey whether or not they would order each type of cuisine. The survey responses are shown in the two-way frequency table.

\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 } \multicolumn{1}{c|}{} & \begin{tabular}{c}
Would Order \\
Italian
\end{tabular} & \begin{tabular}{c}
Would Not \\
Order Italian
\end{tabular} & Total \\
\hline Would Order Chinese & 43 & 25 & 68 \\
\hline Would Not Order Chinese & 20 & 14 & 34 \\
\hline Total & 63 & 39 & 102 \\
\hline
\end{tabular}

Use the table to complete the statements.

The probability that a customer would order Italian is [tex]$\square$[/tex]

The probability that a customer would order Chinese and would not order Italian is [tex]$\square$[/tex]

The probability that a customer would order Italian given that they would not order Chinese is [tex]$\square$[/tex]

Sagot :

GinnyAnsweridn
Certainly! Let's go through the table and calculate the required probabilities step-by-step.

1. Probability that a customer would order Italian:
- From the table, the number of customers who would order Italian is 63.
- The total number of surveyed customers is 102.
- The probability is calculated as:
[tex]\[ P(\text{Order Italian}) = \frac{\text{Number of customers who would order Italian}}{\text{Total number of customers}} = \frac{63}{102} \][/tex]
Simplifying this fraction, we get:
[tex]\[ P(\text{Order Italian}) = 0.618 \][/tex]

2. Probability that a customer would order Chinese and would not order Italian:
- From the table, the number of customers who would order Chinese and would not order Italian is 25.
- The total number of surveyed customers is 102.
- The probability is calculated as:
[tex]\[ P(\text{Order Chinese and not Italian}) = \frac{\text{Number of customers who would order Chinese and not Italian}}{\text{Total number of customers}} = \frac{25}{102} \][/tex]
Simplifying this fraction, we get:
[tex]\[ P(\text{Order Chinese and not Italian}) = 0.245 \][/tex]

3. Probability that a customer would order Italian given that they would not order Chinese:
- From the table, the number of customers who would not order Chinese is 34.
- Out of these, the number of customers who would order Italian is 20.
- The conditional probability is calculated as:
[tex]\[ P(\text{Order Italian} \mid \text{Not Order Chinese}) = \frac{\text{Number of customers who would order Italian and not Chinese}}{\text{Number of customers who would not order Chinese}} = \frac{20}{34} \][/tex]
Simplifying this fraction, we get:
[tex]\[ P(\text{Order Italian} \mid \text{Not Order Chinese}) = 0.588 \][/tex]

So, the completed statements are:
- The probability that a customer would order Italian is 0.618.
- The probability that a customer would order Chinese and would not order Italian is 0.245.
- The probability that a customer would order Italian given that they would not order Chinese is 0.588.
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