Elementary Math: Understanding Probability

Probability is the math of chances. It may be tricky at first, but this will turn out to be a type of math that you will need throughout your life, so it's best to learn it well. Here are some sample problems and examples from real life to smooth the transition to mastering the math of probability.

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Learning Probability

What Is Probability?

Probability measures how likely it is that something will happen. A question might be, how likely is it that the day of the week will begin with an 's'? Well, of course there are seven days in every week, and only Saturday and Sunday begin with 's', so there's a 2/7 chance of landing on a 's' day.

Make Models

One way to visualize probability is to make a pie chart. You can draw one yourself or print one from the Internet. To make your own, use a protractor to draw a large circle on a piece of paper. Divide the circle into four equal quadrants and shade each quarter in with a different color crayon or marker. Let's say you have green, red, purple and orange quadrants.

What are the changes of spinning the circle and landing on a red quadrant? The chance of landing on a red quadrant is the same as the chance of landing on any of the other quadrants, because there are only four and they are all of equal size. The probability is one in four, or 1/4.

Practice Problems

  1. What is the chance of choosing a number including the digit 'three' from a bag that contains the numbers 1-25?
  2. Are you more likely to flip a coin and get 'heads' or win a raffle with 20 people playing?
  3. If there are two girls and three boys playing with a ball, what chance does a girl have of holding the ball at any given moment, assuming they all share the ball equally?


  1. 3/25
  2. You're more likely to get 'heads' because that's a one in two (1/2) chance, whereas the likelihood of winning the raffle is one out of 20 (1/20).
  3. 2/5

Real-life Examples

Probability is one of the math units that we use the most in our everyday lives. Imagine you need to catch a train to the airport for a flight at 5:00 pm. How do you decide which train to take? You have to ask yourself which train will leave latest with the greatest chance of getting you to your flight on time.

If there's a train at 3:00 pm and one at 3:30 pm, you have to evaluate all the possible factors. For instance, traffic and possible train delays help to determine the probability of missing your flight. In the end, you may decide it is a better idea to leave at 3:00.

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