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Lesson 57: Introduction to Probability
Probability is a very big topic in math. It also comes up in everyday life, when we want to know how likely it is that a certain event will occur. This lesson introduces you to the basics.
Probability is the study of how likely (how probable) it is that a particular event will occur. In math, if something is considered to be impossible, we say that is has a probability of 0. For example, if I have a bag of nothing but blue marbles, the chances that I will draw a red one is 0. If something is guaranteed to happen, we say that it has a probability of 1. For example, if a bag has nothing but blue marbles, the chances of drawing a blue one are 1. It is certain, if I choose to draw a marble.
What that means is that if something is only somewhat likely to occur, the probability is represented as a fraction, or as an equivalent decimal or percent. For example, if a bag has 50 red marbles, and 50 blue ones, what is the probability that I will draw a red marble, if I choose to draw one?
To solve this, we must first know how many marbles are in the bag in total. That's easy, there are 100. Now we need to know how many of them will result in success. There are 50 red ones. My chances of drawing a red marble are 50 out of 100. This can be represented as 50/100, or 0.50, or 50%. I could also reduce the fraction to 1/2 (one-half). If I start with a full bag, half of the time, overall, I will draw a red marble. Of course there will not be a perfect pattern. I won't necessarily alternate drawing red and blue marbles. But over the long term, half the time I'll draw a red marble.
Let's try some other examples. If I have a bag of two red marbles, three blue marbles, and three green marbles, what are the chances I will draw a blue marble? There are 8 total marbles, and I'm interested in 3 of them. The probability is 3/8.
Here is a harder one. Let's use the same example, but now I want to know the chances that I will draw either a red marble or a blue marble. We still have 8 marbles in total. How many of them will result in a success? There are 2 reds, and 3 blues. That means five possible marbles resulting in success. The probability is 5/8.
You'll learn much more about probability in later lessons.
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