Question

use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. assume that orders are randomly selected from those included in the table. drive-thru restaurant a b c d order accurate 330 279 245 125 order not accurate 40 54 32 16 if one order is selected, find the probability of getting an order that is not accurate or is from restaurant c. are the events of selecting an order that is not accurate and selecting an order from restaurant c disjoint events? the probability of getting an order from restaurant c or an order that is not accurate is (round to three decimal places as needed.) are the events of selecting an order from restaurant c and selecting an inaccurate order disjoint events? the events dropdown disjoint because it dropdown possible to dropdown

Explanation:

Part 1: Probability Calculation

Step 1: Calculate Total Orders

First, we find the total number of orders by summing all the values in the table.
For Order Accurate: \( 330 + 279 + 245 + 125 = 979 \)
For Order Not Accurate: \( 40 + 54 + 32 + 16 = 142 \)
Total orders \( N = 979 + 142 = 1121 \)

Step 2: Define Events

Let \( A \) be the event that an order is not accurate, and \( B \) be the event that an order is from Restaurant C.

• Number of orders not accurate (\( n(A) \)): \( 142 \)
• Number of orders from Restaurant C (\( n(B) \)): \( 245 + 32 = 277 \)
• Number of orders that are both not accurate and from Restaurant C (\( n(A \cap B) \)): \( 32 \) (since Restaurant C has 32 not accurate orders)

Step 3: Apply Inclusion - Exclusion Principle

The formula for \( P(A \cup B) \) is \( P(A) + P(B) - P(A \cap B) \), where \( P(X)=\frac{n(X)}{N} \)
\( P(A)=\frac{142}{1121} \), \( P(B)=\frac{277}{1121} \), \( P(A \cap B)=\frac{32}{1121} \)
\( P(A \cup B)=\frac{142 + 277- 32}{1121}=\frac{142 + 245}{1121}=\frac{387}{1121}\approx0.345 \) (rounded to three decimal places)

Part 2: Disjoint Events

Two events are disjoint if they cannot occur at the same time, i.e., \( A\cap B=\varnothing \) (the intersection has no elements). Here, we have \( n(A\cap B) = 32
eq0 \), which means there are orders that are both not accurate and from Restaurant C. So the events are not disjoint.

Answer:

The probability of getting an order from Restaurant C or an order that is not accurate is \(\boldsymbol{0.345}\) (rounded to three decimal places).

Are the events of selecting an order from Restaurant C and selecting an inaccurate order disjoint events?

The events \(\boldsymbol{\text{are not}}\) disjoint because it \(\boldsymbol{\text{is}}\) possible to \(\boldsymbol{\text{select an order that is both not accurate and from Restaurant C}}\).