Question

If 3 out of 8 drivers exceed the speed limit on a given stretch of highway, what is the chance that a speed camera will catch a speeder if it photographs a car at random? Give your answer to the nearest tenth of a percent. (A) 30.0% (B) 37.5% (C) 42.5% (D) 45.0%

Short answer

(B) 37.5%

Step-by-step solution

Identify the number of speeders and total drivers

In this problem, we are given that 3 out of 8 drivers exceed the speed limit. So, the number of speeders is 3, and the total number of drivers is 8.

Calculate the probability of catching a speeder

To calculate the probability of catching a speeder, we need to divide the number of speeders by the total number of drivers. Probability = \(\frac{Number\ of\ speeders}{Total\ number\ of\ drivers}\)

Plug in the numbers and solve for the probability

Now, we will substitute the number of speeders (3) and total drivers (8) into our formula and calculate the probability. Probability = \(\frac{3}{8}\)

Convert the probability to a percentage

To convert the probability to a percentage, multiply it by 100. Percentage = Probability × 100 Percentage = \(\frac{3}{8}\) × 100

Round the percentage to the nearest tenth

Now, we need to round the percentage to the nearest tenth. Percentage = 37.5% So, the chance that a speed camera will catch a speeder if it photographs a car at random is 37.5%. The correct answer is (B) 37.5%.

Key concepts

GED Math Practice

GED (General Educational Development) math practice involves familiarizing oneself with a variety of mathematical concepts and problems similar to those that appear on the actual GED test. It's crucial for students to understand problem-solving strategies across different math topics, including algebra, geometry, and data analysis.

One common type of question encountered in GED math practice is probability calculation. These questions test a student's ability to apply mathematical reasoning to real-world scenarios. To enhance GED math skills, students should practice working through problems methodically, as shown in the step-by-step solution given for the exercise on the probability of a speed camera catching speeders. By repeatedly practicing problems of this nature, students solidify their understanding and improve their speed and accuracy in problem-solving.

Percentage Conversion

Percentage conversion is a critical skill not only in math classes but in everyday life, as percentages are used widely in statistics, finance, and various measurements. To convert a probability or a fraction to a percentage, as seen in our exercise, you must multiply it by 100. This process transforms a fraction such as \(\frac{3}{8}\), which is abstract for many, into a more tangible and universally understood figure, like 37.5%.

It's important to remember that percentages are actually parts per hundred, helping to express one quantity as a fraction of another. When improving percentage conversion skills, students should ensure they understand both the multiplication by 100 conceptually and the practical method—for instance, moving the decimal point two places to the right.

Probability Questions

Probability questions are a staple in many mathematics courses, as they deal with the likelihood of events happening. They often require a combination of counting principles, understanding of fractions, and sometimes, knowledge of event independence or dependence.

The core of these questions is the probability formula which states that the probability of an event is equal to the number of successful outcomes divided by the total number of possible outcomes. Familiarity with simple probability problems, such as calculating the chance that a speed camera will catch a speeder, serves as a foundation for more complex probability calculations encountered in advanced mathematics and statistics.