In Exercises 11–16, a die is rolled. Find the probability of getting a number greater than 4.

검증된 단계별 안내

Identify the total number of possible outcomes when rolling a standard die. Since a die has 6 faces, the total number of outcomes is \(6\).

Determine the favorable outcomes for the event "getting a number greater than 4." The numbers greater than 4 on a die are \(5\) and \(6\).

Count the number of favorable outcomes. There are \(2\) such numbers: \(5\) and \(6\).

Use the probability formula: \(\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\).

Substitute the values into the formula: \(\text{Probability} = \frac{2}{6}\). This fraction can be simplified if needed.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Sample Space

The sample space is the set of all possible outcomes of an experiment. For a single roll of a standard die, the sample space consists of the numbers {1, 2, 3, 4, 5, 6}. Understanding the sample space is essential to determine the total number of possible outcomes.

Event

An event is a subset of the sample space that includes outcomes of interest. In this problem, the event is rolling a number greater than 4, which includes the outcomes {5, 6}. Identifying the event helps in calculating the probability.

Probability Calculation

Probability is calculated as the ratio of favorable outcomes to the total number of possible outcomes. Here, the probability of rolling a number greater than 4 is the number of favorable outcomes (2) divided by the total outcomes (6), resulting in 2/6 or 1/3.