Question

type the correct answer in the box. use numerals instead of words. for this question, an answer that is not a whole number should be entered as a decimal, rounded 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. use the table to complete the statements. the probability that a customer would order italian is . the probability that a customer would order chinese and would not order italian is . the probability that a customer would order italian given that they would not order chinese is .

	would order chinese	would not order chinese	total
would not order italian	25	14	39
total	68	34	102

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of frequencies in a two - way table, if we want to find the probability that a customer would order Italian given that they would not order Chinese, we use the formula $P(\text{Italian}|\text{Not Chinese})=\frac{n(\text{Italian and Not Chinese})}{n(\text{Not Chinese})}$.

Step2: Identify relevant values from the table

The number of customers who would not order Chinese is $n(\text{Not Chinese}) = 34$. The number of customers who would not order Chinese and would order Italian is $n(\text{Italian and Not Chinese}) = 20$.

Step3: Calculate the probability

$P(\text{Italian}|\text{Not Chinese})=\frac{20}{34}\approx0.588$

The probability that a customer would order Chinese and would not order Italian is calculated as follows:

Step1: Recall the formula for probability

The probability $P$ of an event is $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. We want to find $P(\text{Chinese and Not Italian})$.

Step2: Identify relevant values from the table

The number of customers who would order Chinese and not order Italian is $25$, and the total number of customers is $102$.

Step3: Calculate the probability

$P(\text{Chinese and Not Italian})=\frac{25}{102}\approx0.245$

The probability that a customer would order Italian is calculated as follows:

Step1: Recall the formula for probability

$P(\text{Italian})=\frac{n(\text{Italian})}{n(\text{Total})}$.

Step2: Identify relevant values from the table

The number of customers who would order Italian is $63$, and the total number of customers is $102$.

Step3: Calculate the probability

$P(\text{Italian})=\frac{63}{102}\approx0.618$

Answer:

The probability that a customer would order Italian given that they would not order Chinese is approximately $0.588$.
The probability that a customer would order Chinese and would not order Italian is approximately $0.245$.
The probability that a customer would order Italian is approximately $0.618$.