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Chapter 9: Problem 17

If a single die is rolled, what is the probability that it will come up with an even number?

Short Answer

Expert verified
The probability of rolling an even number is 0.5.

Step by step solution

01

Identify total possible outcomes

A single die has 6 faces. When rolled, it can land on any one of these faces: 1, 2, 3, 4, 5, or 6. Therefore, the total number of possible outcomes is 6.
02

Identify favorable outcomes

An even number on a die includes 2, 4, and 6. Therefore, there are 3 favorable outcomes.
03

Calculate the probability

Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes. So, the probability is \(\frac{3}{6}\) which simplifies to \(\frac{1}{2}\).
04

Express as a decimal

To express the probability as a decimal, divide 3 by 6 to get 0.5.

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Key Concepts

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

Single Die
A die, often referred to as a single die, is a small cube with 6 faces, each marked with a different number from 1 to 6. When you roll a single die, it lands on one of these six faces. This roll is a random event because each face has an equal chance of landing face up. Rolling a die is a common example used to explain basic concepts in probability since it clearly illustrates the idea of random outcomes.
Favorable Outcomes
In probability, a 'favorable outcome' is an outcome that satisfies the event you are interested in. For this exercise, the event of interest is rolling an even number. On a single die, the favorable outcomes are the faces that show an even number. These are 2, 4, and 6. So, there are 3 favorable outcomes. Identifying these outcomes helps us calculate the probability of an event occurring.
Possible Outcomes
Possible outcomes are all the different results that can occur in a probability event. For a single die, the total number of possible outcomes is 6 because there are 6 faces (1, 2, 3, 4, 5, and 6). Understanding the total number of possible outcomes is essential because it forms the denominator when calculating the probability of a favorable event. Thus, for a single die, there are 6 possible outcomes.
Decimal Representation
Decimal representation is a way of expressing fractions in decimal form. To calculate the decimal representation of a probability, divide the number of favorable outcomes by the total number of possible outcomes and simplify if necessary. For example, in this exercise:
  • Number of favorable outcomes: 3 (for even numbers on a die)
  • Total possible outcomes: 6
The probability as a fraction is \(\frac{3}{6}\), which simplifies to \(\frac{1}{2}\). Turning this into a decimal, we get 0.5. This makes it easier to understand and compare probabilities.

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