Math Problem Statement

What is the probability that the driver was not intoxicated but the pedestrian was intoxicated, based on the given data?

Solution

Let's solve this step by step!

Problem Breakdown:

We are tasked with finding the probability that the driver was not intoxicated but the pedestrian was intoxicated, based on the given data table.

Step 1: Extract data from the table.

From the table:

  • Driver NOT Intoxicated AND Pedestrian Intoxicated: This corresponds to 270 cases.
  • Total number of cases: 978 (sum of all rows and columns in the table).

Step 2: Probability Formula.

The probability of a specific event occurring is:

P=Favorable CasesTotal CasesP = \frac{\text{Favorable Cases}}{\text{Total Cases}}

Here: P=270978P = \frac{270}{978}

Step 3: Perform the Calculation.

P=2709780.2761P = \frac{270}{978} \approx 0.2761

Convert this to a percentage: P×100=27.6%P \times 100 = 27.6\%

Final Answer:

The probability is 27.6%.

Let me know if you would like further explanation or have any follow-up questions. 😊


5 Related Questions:

  1. How do you calculate the probability of multiple events using conditional probabilities?
  2. What is the difference between independent and dependent events in probability?
  3. How do you calculate complementary probabilities (e.g., if the driver is intoxicated)?
  4. How can this type of table be used to determine if two events are independent?
  5. How do you round percentages to a specified decimal place?

Tip:

When working with percentages, always ensure the decimal point placement is correct and double-check your rounding method!

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Math Problem Analysis

Mathematical Concepts

Probability
Conditional Probability

Formulas

P = Favorable Cases / Total Cases

Theorems

Basic Probability Theorem

Suitable Grade Level

Grades 7-9