In Exercises 49–52, a single die is rolled twice. Find the probability of rolling an even number the first time and a number greater than 2 the second time.

검증된 단계별 안내

Identify the sample space for each roll of the die. Since a single die has 6 faces, each roll has 6 possible outcomes: 1, 2, 3, 4, 5, and 6.

Determine the favorable outcomes for the first roll: rolling an even number. The even numbers on a die are 2, 4, and 6, so there are 3 favorable outcomes.

Determine the favorable outcomes for the second roll: rolling a number greater than 2. The numbers greater than 2 are 3, 4, 5, and 6, so there are 4 favorable outcomes.

Calculate the probability of each event separately. The probability of rolling an even number first is \(\frac{3}{6}\), and the probability of rolling a number greater than 2 second is \(\frac{4}{6}\).

Since the two rolls are independent events, multiply the probabilities of each event to find the combined probability: \(\frac{3}{6} \times \frac{4}{6}\).

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.

Probability of Independent Events

When two events occur independently, the probability of both happening is the product of their individual probabilities. Rolling a die twice are independent events, so multiply the probability of the first event by the probability of the second.

Sample Space of a Die Roll

A single roll of a fair six-sided die has six equally likely outcomes: 1 through 6. Understanding this sample space helps determine the probability of specific events, such as rolling an even number or a number greater than 2.

Event Definition and Counting Favorable Outcomes

To find the probability of an event, identify all outcomes that satisfy the event's condition. For example, even numbers on a die are 2, 4, and 6; numbers greater than 2 are 3, 4, 5, and 6. Counting these helps calculate the event's probability.