Question

Find the probability of the event. Rolling an even number using a six-sided number cube.

Short answer

The probability of rolling an even number using a six-sided number cube is 0.5

Step-by-step solution

Determine the total number of outcomes

When a six-sided number cube (commonly referred to as a dice) is rolled, the total outcomes are 6; each side of the dice represents one possible outcome, and the cube has six sides.

Determine the favorable outcomes

In this case, the event we're interested in is rolling an even number. A cube has 3 even numbers - 2, 4, 6. Therefore, the number of favorable outcomes is 3.

Calculate the probability

Probability is calculated using the formula: Probability of an Event = (Number of Favorable Outcomes) / (Total Number of Outcomes) = 3 / 6 = 0.5

Key concepts

Probability of an Event

Understanding the probability of an event is crucial for students navigating the world of algebra and statistics. Probability measures how likely it is for an event to occur, often expressed as a number between 0 and 1, where 0 indicates impossibility, and 1 signifies certainty. For example, when you roll a six-sided number cube, there's a probability attached to the event that an even number will land facing up. This probability is derived from comparing the favorable outcomes to the total possible outcomes. In educational terms, we can think of it as the 'chance' of your desired outcome happening based on all possible outcomes. To ensure students fully grasp this concept, we demonstrate through practical examples, such as the roll of a die. This engages the learners and cements understanding by showing them real-life applications of theoretical mathematical concepts.

Favorable Outcomes

A favorable outcome is one that matches the criteria of the event being considered. In our dice-rolling exercise, the favorable outcomes are the even numbers: 2, 4, and 6. Identifying these outcomes is an essential step in problem-solving related to probability. It's worth noting that a comprehensive understanding of what constitutes a favorable outcome helps students solve more complex problems with confidence. Using simple and relatable scenarios, such as games involving dice, cards, or coins, can significantly improve students' ability to identify and count favorable outcomes. For instance, in dice games, we specifically list the outcomes that meet our criteria, thus making the problem-solving process more transparent and accessible.

Total Number of Outcomes

The total number of outcomes is an all-inclusive count of all the possible results that can emerge from a probabilistic event. When rolling a six-sided number cube, the total number of outcomes is six because there are six faces that the die could land on. Knowing this total is vital for calculating the probability of events. To enhance students' understanding, the concept of total outcomes can be expanded to include more complex situations like multiple dice rolls or drawing cards from a deck. By engaging with such problems, students develop the skills to systematically count and consider all possible outcomes before calculating probabilities.