2. Determine whether each number could represent the probability ...

4. Probability

Basic Concepts of Probability

Statistics

4. Probability

Basic Concepts of Probability

1:58 minutes

Problem 3.1.2a

Textbook Question

2. Determine whether each number could represent the probability of an event. Explain your reasoning. a. 25/25

Verified step by step guidance

Step 1: Recall the definition of probability. Probability is a measure of the likelihood of an event occurring, and it is always a value between 0 and 1, inclusive. This means probabilities cannot be negative or greater than 1.

Step 2: Simplify the given fraction, 25/25. Perform the division to determine its value. Mathematically, dividing any number by itself results in 1.

Step 3: Compare the simplified value (1) to the range of valid probabilities (0 ≤ P ≤ 1). Since 1 is within this range, it is a valid probability.

Step 4: Explain the reasoning. A probability of 1 indicates that the event is certain to occur. For example, if you have 25 favorable outcomes out of 25 possible outcomes, the event is guaranteed to happen.

Step 5: Conclude that the number 25/25 could represent the probability of an event because it simplifies to 1, which is within the valid range for probabilities.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability Range

Probability is a measure of the likelihood of an event occurring, and it is always expressed as a number between 0 and 1. A probability of 0 indicates that an event will not occur, while a probability of 1 indicates certainty that the event will occur. Any value outside this range is not valid for representing probabilities.

Fraction Representation

Fractions can be used to express probabilities, where the numerator represents the number of favorable outcomes and the denominator represents the total number of possible outcomes. In the case of 25/25, this fraction simplifies to 1, which is a valid probability indicating certainty that the event will occur.

Interpretation of Probabilities

Understanding how to interpret probabilities is crucial. A probability of 1 (or 100%) means that the event is guaranteed to happen, while a probability of 0 (or 0%) means it cannot happen. Therefore, when evaluating whether a number can represent a probability, it is essential to consider its meaning in the context of possible outcomes.

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