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Chapter 4: Problem 22

In a group of 50 car owners, 8 own hybrid cars. If one car owner is selected at random from this group, what is the probability that this car owner owns a hybrid car?

Short Answer

Expert verified
The probability that a randomly selected car owner from this group owns a hybrid car is 0.16.

Step by step solution

01

Identify the Number of Successful Outcomes

The number of successful outcomes is the number of hybrid car owners, which is 8.
02

Identify the Total Number of Outcomes

The total number of outcomes is the total number of car owners, which is 50.
03

Calculate the Probability

The probability is calculated by dividing the number of successful outcomes by the total number of outcomes. So the result will be \( \frac{8}{50} = 0.16 \)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Successful Outcomes
When dealing with probability problems, the concept of "successful outcomes" is crucial. Successful outcomes refer to the number of outcomes that satisfy the given condition or event.

In the context of our car owners example, the successful outcome is when a randomly selected owner is a hybrid car owner. There are 8 hybrid car owners in the group. So, the number of successful outcomes is 8.

To determine successful outcomes, it's important to clearly understand the event or condition you are evaluating. Sometimes, it helps to make a list or use a simple tally to count the outcomes that meet your criteria. This is a fundamental step for correctly calculating probability.
Total Outcomes
The term "total outcomes" signifies all possible or complete outcomes for a given problem or situation. In probability, this typically refers to the total number of different ways an event can occur.

In the example, the total outcomes encompass all 50 car owners because a selection is made randomly among them. Understanding and identifying the total number of outcomes is vital for computing probability.

Remember, in probability, we always place successful outcomes over total outcomes to form a ratio. A common mistake is to confuse or inaccurately determine the total outcomes, leading to incorrect probability values.
Random Selection
Random selection plays a key role in probability calculations. It implies that every individual or item in a set has an equal chance of being chosen.

With random selection, there is no bias or preference influencing which item is selected. Consider our car owners scenario. Each of the 50 owners has an equal opportunity to be selected, which legitimizes the probability calculation.

Being aware of random selection helps ensure fairness and randomness in experiments or selections. It is a foundation of probability theory, guiding us to interpret and trust the results we compute using probability methods.

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Most popular questions from this chapter

A die is rolled once. What is the probability that a. a number less than 5 is obtained? b. a number 3 to 6 is obtained?

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A box contains three items that are labeled \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\). Two items are selected at random (without replacement) from this box. List all the possible outcomes for this experiment. Write the sample space.
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