Скачать или смотреть visual math: simplified conditional probability with one die

Welcome to our visual math video where we simplify the concept of conditional probability using a single die. 🎲 In this video, we explore the fundamental ideas behind conditional probabilities and how they relate to dice rolls. We begin by considering the six basic faces of a die 1️⃣ 2️⃣ 3️⃣ 4️⃣ 5️⃣ 6️⃣.

Let's dive into an example scenario. Suppose the question is, "What's the probability of rolling a two, given that the number of dots on the face is even?" 🎲|◻️. To solve this, we focus on the even-numbered faces and count how many of them satisfy this condition. As we can see, three faces have an even number of dots 2️⃣ 4️⃣ 6️⃣. These three faces represent our reduced sample space.

Next, we determine how many of these three faces correspond to the desired outcome, which in this case is rolling a two. Out of the three even-numbered faces, only one face shows a two 2️⃣. Therefore, the probability of rolling a two, given an even number of dots, is 1️⃣/3️⃣. 🎲|◻️ = 1️⃣/3️⃣.

Now, let's explore another scenario. Consider the probability of rolling a five, given that the number of dots on the face is greater than or equal to three. 🎲|◻️ ≥ 3️⃣. First, we mark the reduced sample space, which includes four faces that have three or more dots 3️⃣ 4️⃣ 5️⃣ 6️⃣. The face corresponding to a five is the only one in this reduced sample space, making the probability simply 1️⃣/4️⃣. 🎲5️⃣|◻️ ≥ 3️⃣ = 1️⃣/4️⃣.

In a more involved example, let's determine the probability of rolling a one or a two, given that the number of dots on the face is less than or equal to three. 🎲|◻️ ≤ 3️⃣. We begin by marking the reduced sample space, which consists of the first three faces 1️⃣ 2️⃣ 3️⃣. Out of these three faces, only two correspond to a one or a two 1️⃣ 2️⃣. Hence, the probability is 2️⃣/3️⃣. 🎲1️⃣2️⃣|◻️ ≤ 3️⃣ = 2️⃣/3️⃣.

These examples demonstrate the underlying concepts of conditional probabilities. We establish a reduced sample space based on a given condition and then calculate the probability within that smaller sample space. Remember, conditional probability allows us to make more accurate predictions by considering specific conditions. 🎲🔍

Thank you for watching our visual math video! Stay tuned for more exciting concepts and problem-solving techniques. Don't forget to like, subscribe, and leave your comments below! Happy learning! 🎲📚

🎲🔍📚 15 Common Internet Questions about Conditional Probability

1️⃣ What is conditional probability?
Answer Conditional probability refers to the probability
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