Probability - Concept
Adding and subtracting rational expressions is similar to adding fractions. When adding and subtracting rational expressions, we find a common denominator and then add the numerators. To find a common denominator, factor each first. This strategy is especially important when the denominators are trinomials.
You guys probably already know a lot about how to calculate probabilities. It's a good idea to continue to learn how to do probabilities well because they're going to show up a lot in your Math career through high school. You guys probably already know the definition. The probability of an event happening, is probably of that event is equal to the fraction, number of successful outcomes divided by number of possible outcomes.
Couple of things I want to point out to you first thing the probability of an event an event is like a different word for an outcome. Also look at this notation p and then parentheses with usually some kind of a word in there, that doesn't mean multiply p times something that means you're probably going to write it in words. Your answer will look like p parentheses some words equals some number. Also when we talk about successful outcomes and possible outcomes that's things like let's say you're rolling a die where it has 6 sides and you want to get a 1. Number of successful outcomes would be the success. You got the one, number of possible outcomes represents there are 6 sides on that die.
Another important things I have here in red is that this formula is only true if your outcomes are all equally likely. If some of them are not equal as others or is equally likely to happen as others it's going to be a lot trickier. Last thing I want to leave you with is a new definition about a complement, the complement of an event is the probability that the event does not occur. Like let's say the weather forecast is 80% chance of rain then we would say the complement is the probability that it does not rain. 80% chance of rain means 20% chance that it does not rain. That's a complement and the way you find it out is by doing 100% take away the percent of your event will give you the complement. That's what we did in our situation 100 take away the probability of that event is equal to the probability that the event does not happen or the complement.
The last thing I want you guys to think about before you do your homework problems is how you're going to write your answers. Probability should always come out as a number thats between zero and 1. I'm going to write it like this probability should always be between zero and 1. It might equal zero it might equal 1. So you're either going to have a decimal, a fraction or a percent as your final answer. It's really important that you guys are comfortable moving through all 3 of those different representations of your answer numbers.