A die is rolled. Find the probability of getting a number less than 5.

검증된 단계별 안내

Step 1: Understand the problem. A standard die has 6 faces numbered 1 through 6. The goal is to find the probability of rolling a number less than 5.

Step 2: Identify the favorable outcomes. Numbers less than 5 on a die are 1, 2, 3, and 4. This gives us 4 favorable outcomes.

Step 3: Determine the total possible outcomes. Since a die has 6 faces, there are 6 possible outcomes in total.

Step 4: Use the probability formula: \( P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \). Substitute the values: \( P(E) = \frac{4}{6} \).

Step 5: Simplify the fraction if necessary. \( \frac{4}{6} \) can be simplified to \( \frac{2}{3} \). This represents the probability of rolling a number less than 5.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. An event with a probability of 0 means it will not happen, while a probability of 1 means it will certainly happen. In this context, we are interested in the probability of rolling a number less than 5 on a standard six-sided die.

Sample Space

The sample space is the set of all possible outcomes of a random experiment. For a single roll of a six-sided die, the sample space consists of the numbers {1, 2, 3, 4, 5, 6}. Understanding the sample space is crucial for calculating probabilities, as it provides the total number of outcomes against which specific events can be measured.

Favorable Outcomes

Favorable outcomes refer to the specific outcomes in the sample space that satisfy the condition of the event we are interested in. In this case, the favorable outcomes for rolling a number less than 5 are {1, 2, 3, 4}, which totals four outcomes. The probability of the event is calculated by dividing the number of favorable outcomes by the total number of outcomes in the sample space.