The probability of red is 2/5. What is the probability of not red
视频信息
答案文本
视频字幕
Probability is a measure of how likely an event is to occur, ranging from 0 for impossible events to 1 for certain events. In this problem, we're told that the probability of red is 2/5, or 0.4. Let's visualize this on a probability scale.
Complementary events are two outcomes that together make up all possible outcomes. For any event, its complement includes everything else that could happen. The key principle is that the probabilities of complementary events always sum to 1. So if we know the probability of red, we can find the probability of not red.
We can visualize probability problems in multiple ways to enhance understanding. Here are three methods: First, a pie chart showing 2/5 red and 3/5 not red. Second, a probability bar divided proportionally. Third, a grid model with 10 squares where 4 are red and 6 are not red. All these visual methods lead to the same mathematical conclusion.
Now let's apply the complementary probability formula to solve this problem. Step 1: We know that P of red equals 2/5. Step 2: The formula for complementary probability is P of not red equals 1 minus P of red. Step 3: Substituting our value, we get 1 minus 2/5. Step 4: Converting 1 to fifths, we have 5/5 minus 2/5. Step 5: Subtracting gives us 3/5. Finally, we can verify our answer: 2/5 plus 3/5 equals 5/5, which equals 1.
The complementary probability principle applies to many real-world scenarios. First, drawing colored balls from a bag: if 2 out of 5 balls are red, then 3 out of 5 are not red. Second, spinning a colored wheel: if 40% of the wheel is red, then 60% is not red. Third, selecting colored cards: if 2 out of 5 cards are red, then 3 out of 5 are not red. In each case, knowing one probability immediately gives us the complementary probability.
Let's work through some practice problems to solidify our understanding. Problem 1: If the probability of blue is 3/7, what is the probability of not blue? Solution: 1 minus 3/7 equals 4/7. Problem 2: If the probability of success is 0.4, what is the probability of failure? Solution: 1 minus 0.4 equals 0.6. Problem 3: If the probability of not green is 5/8, what is the probability of green? Solution: 1 minus 5/8 equals 3/8. These examples show the consistent application of the complement rule.
Let's summarize the key concepts. First, complementary events always sum to 1. Second, the complement formula is P of not A equals 1 minus P of A. Third, always verify your answer by checking that P of A plus P of not A equals 1. Applying these principles to our problem, we've determined that the probability of not red is 3/5. This is visually represented in our pie chart showing 2/5 red and 3/5 not red.