The probability of red is 3/6. What is the probability of not red
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Probability is a measure of how likely an event is to occur. It ranges from 0, meaning the event is impossible, to 1, meaning the event is certain. The basic probability formula is the number of favorable outcomes divided by the total number of possible outcomes. For example, when flipping a fair coin, the probability of getting heads is one half because there is one favorable outcome out of two total outcomes.
We are given that the probability of red is three sixths. This is written mathematically as P of red equals three sixths. This fraction can be simplified to one half. To visualize this, imagine we have six equal sections, and three of them are colored red. The other three sections are different colors, representing the outcomes that are not red.
Complementary events are two mutually exclusive events that together cover all possible outcomes. For any event A, its complement, written as not A, includes all outcomes that are not in A. A key property is that the probability of an event and its complement always sum to one. This relationship is expressed by the formula: P of A plus P of not A equals one.
Now we can calculate the probability of not red using the complement rule. The complement rule states that the probability of not red equals one minus the probability of red. Substituting our known value, we have one minus three sixths. To subtract these fractions, we convert one to six sixths. This gives us six sixths minus three sixths, which equals three sixths. Simplifying this fraction, we get one half. Therefore, the probability of not red is one half.
Let's verify our answer using different visual models. In a pie chart, we can see that red and not red each take up exactly half of the circle, confirming that both probabilities are one half. In a bar chart, the bars for red and not red are of equal height, again showing they each have a probability of one half. When we add these probabilities together, one half plus one half equals one, which confirms our answer is correct because all probabilities must sum to one.
Let's apply the complement rule to similar problems. If the probability of blue is two eighths, what is the probability of not blue? Using the complement rule, P of not blue equals one minus P of blue. Substituting our value, we have one minus two eighths. Converting one to eight eighths, we get eight eighths minus two eighths, which equals six eighths. Simplifying this fraction by dividing both numerator and denominator by two, we get three fourths. So the probability of not blue is three fourths.
Let's summarize the key takeaways. The complement rule is a fundamental principle in probability. It states that for any event A, the probability of A plus the probability of not A always equals one. This means we can always find the probability of a complement by subtracting the original probability from one. In our problem, since the probability of red was three sixths or one half, the probability of not red is also one half. These two probabilities sum to one, confirming our answer is correct.