Math Problem Statement

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

317317

275275

237237

139139

Order Not Accurate

3737

5555

4040

1313

If one order is​ selected, find the probability of getting an order that is not accurate.

Question content area bottom

Part 1

The probability of getting an order that is not accurate is

enter your response here.

Solution

To find the probability of getting an order that is not accurate, we need to calculate the ratio of the total number of "not accurate" orders to the total number of orders.

Step 1: Sum the "not accurate" orders

The "not accurate" orders for each restaurant are:

  • Restaurant A: 37
  • Restaurant B: 55
  • Restaurant C: 40
  • Restaurant D: 13

Total "not accurate" orders = 37+55+40+13=14537 + 55 + 40 + 13 = 145

Step 2: Sum the total number of orders

The total number of orders (both accurate and not accurate) for each restaurant is:

  • Restaurant A: 317+37=354317 + 37 = 354
  • Restaurant B: 275+55=330275 + 55 = 330
  • Restaurant C: 237+40=277237 + 40 = 277
  • Restaurant D: 139+13=152139 + 13 = 152

Total number of orders = 354+330+277+152=1113354 + 330 + 277 + 152 = 1113

Step 3: Calculate the probability

The probability of selecting a "not accurate" order is the ratio of "not accurate" orders to the total number of orders:

P(not accurate)=1451113P(\text{not accurate}) = \frac{145}{1113}

Now, let's simplify this fraction.

P(not accurate)0.1303P(\text{not accurate}) \approx 0.1303

So, the probability of getting an order that is not accurate is approximately 0.1303, or 13.03%.


Would you like more details on the steps? Here are five related questions to expand on this concept:

  1. What is the probability of getting an accurate order instead?
  2. If two orders are selected at random, what is the probability that both are accurate?
  3. How would the probability change if Restaurant D increased its accurate orders?
  4. What is the combined probability of getting a not accurate order from Restaurants A or B?
  5. How does the accuracy rate vary across restaurants?

Tip: Probability is always a number between 0 and 1, where 0 means impossible and 1 means certain.

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Math Problem Analysis

Mathematical Concepts

Probability
Ratio and Proportion

Formulas

P(event) = Number of favorable outcomes / Total number of outcomes

Theorems

Basic Probability Theorem

Suitable Grade Level

Grades 6-8