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.
