Statistics: Basic Concepts: What is Probability?

Lesson 14: What is Probability?


What is probability?

Probability is an important part of our daily lives. What are the chances it’s going to rain? What are the chances of winning the lottery? While we can try to predict these things, calculating exactly how likely something is to happen–or its probability–can help us to make good decisions.

How to calculate probability

Oftentimes probability is presented as a fraction. We have a numerator (top number) and a denominator (lower number). The numerator reflects what we want to happen–or the number of favorable outcomes–while the denominator reflects the total number of possible outcomes.

Consider this example: there are 9 marbles in a bag. All of them are green, blue, or red. Your friend tells you that if you draw 1 red marble out of the bag, he’ll give you some free cash.

You know that there are 9 marbles in the bag, and 3 of them are red–but you’re not allowed to look when you draw one out. Let’s go over the steps to calculate the probability as a fraction:

  • Step 1: The denominator is the total number of marbles, regardless of their color. 

  • Step 2: For the numerator, write the number of red marbles in the bag. 

  • Step 3: This gives you your fraction, 3/9. So your chances of drawing a red marble are 3 out of 9. But we might have a hard time understanding what this means, so let’s take it a step further…
  • Step 4: Since 3 and 9 are both multiples of 3, you can simplify your fraction by dividing the numerator and denominator by 3.

  • Step 5: So the chances of drawing a red marble is 3/9 or 1/3. The simplified fraction gives us a better sense of the probability. 

If you were trying to determine the probability of drawing the other colors, remember that the number of one color is the numerator, and 9 would stay the denominator.

For example, if you have 1 green marble, then your probability of drawing this color is 1/9. 5 blue marbles means your probability is 5/9. So if you have your choice of which marble to draw for the free cash, go with the blue, since this probability is the highest!

Decimals and percentages

  • Sometimes you cannot simplify a fraction, like 1/9 or 5/9. However, you can always change a fraction into a decimal, and then the decimal into a percentage. For 1/9, 1 ÷ 9 = 0.111 repeating, and 5/9 = 5 ÷ 9 = 0.555 repeating.
  • If you move the decimal over two places to the left, 0.111 → 11.1% and 0.555 → 55.5%. These percentages should give you a better sense of what 1/9 and 5/9 represent in terms of probability.

Hopefully you’ve found this tutorial informative. Be sure to take our final quiz to see how much you’ve learned!