Math SATs- Simple Probability
Welcome to a Math SAT Preparation Lesson. In this lesson we will study the basics of a concept called probability.
Ever wondered what's the probability of the rain in Spain not staying mainly in the plain? Well, I can't tell you that, but I can (probably) tell you what it means.
Let's start off by defining probability
Probability measures how likely something is to happen or not happen. For a very simple example, consider the coin that's in my pocket. If I flip it, it's as probable that I get heads as it is that I get tails. Therefore, there is a 50% chance of me getting heads and a 50% chance of getting tails, and the odds of getting heads vs. tails (or, in this case, tails vs. heads) are 1:1.
Another example- dice. I roll a die (singular for dice, see the vocabulary SAT prep for more info). There's clearly a 1 out of 6 chance that I get 5 in this roll (let's assume the die's weight is evenly distributed).
Now let's look over the first important concept- Or.
In probability studies, or is treated as +, that's the key to remember. For example, what is the probability of rolling a 5 or a 6 using a normal die? Well, there's a 1/6 chance for either one, so for getting 5 OR 6 I have a probability of 1/6 for rolling a 5, plus the probability of 1/6 for rolling a 6 (since both events can't happen at the same time). Thus, the probability is now 2/6, or 1/3.
It's important to note a few things. First, the probabilities of all of the possible outcomes of one event always add up to 1. Also, if the probability of something happening is X, the probability of that thing not happening is 1-X. For example, if there's a 20% of rain today, there's an 80% it won't rain today. This doesn't mean anything about whether it will be sunny, snowy or windy, but it does mean that there's 80% of no rain.
Moving on, here's our second important concept- And.
And means times, or multiply. For example, say I flip a coin twice. What's the probability of getting 2 heads in a row? Well, the probability for the first heads is 1/2, and so is the probability for the second one. So if we want one heads AND another one, we multiply them together to get 1/4. Still not convinced? Draw a possibility tree. This tree shows all the possible outcomes, but sadly I have no idea of how to draw a tree here yet, so we'll just write them down: tails-tails, heads-tails, tails-heads and heads-heads. So, since all possibilities are equally likely, we do have a 1 in 4 chance.
So, if we're looking at the probability of option A or of option
B, we've got . If we want A and B, it's
.
As you've already noticed, probabilities come in various shapes. We can have them as fractions, percentages, or decimal places. Try not to let it confuse you too much.
Probabilities are used in real life to approximate amounts of stuff. For instance, say I know that the probability of a person having blue eyes is 1/4. Then if I'm working with 20 other people, I can expect that about 5 of them should have blue eyes. Makes sense, doesn't it?
That's it, really.
Probability isn't complicated if you remember the difference
between and and or. If you
think you do, go and have some practice with the all-new probability
test.
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