How to Calculate Probability

By: Shawn Donovan,

Chances are you need help to calculate probability. Statistical probability can be a tricky subject. But with a little help, the odds are high that you'll be able to find probability answers quickly and easily.

Probability Defined
Probability is the likelihood of an event occurring divided by the number of possible outcomes. That may sound a little confusing, so let's break it down into simpler terms with an example.

Say you have a quarter. If you flip it in the air, what's the likelihood that it will land on heads? One side of the coin is heads and the other is tails. So the total number of outcomes is two, heads or tails. The likelihood of it landing on heads is one, because there is only one heads side. So you just figured out the probability of a coin landing on heads is 1:2, or half of the time.

What if you flipped the coin and it has landed on tails 8 times in a row? What is the probability of the coin landing on heads in the next flip? The answer is still 1:2. Because each event is unique, it doesn't matter how many times it lands on tails, the probability of it being heads is still the same.

Complex Probability
While the basic rules of probabilty are always the same, the math gets a little trickier when the numbers get bigger. Consider a deck of cards. A deck contains 52 cards, with 4 suits: clubs, hearts, diamonds and spades. There are 13 cards in each suit.

Shuffle the deck and pick one card out. What is the probability that the card you chose is a club? In order to calculate probability, you need to know how often an event can occur and how many possible outcomes exist. Since there is a total number of 52 cards in the deck, that is the total number of outcomes. The likelhood of the card you picked being a club depends on the number of clubs in the deck. We know that there are 13 clubs in a deck. Your answer is 13:52, which reduces to a 1 in 4 chance of choosing a club. If you put that card back in the deck and reshuffle, you know your odds will remain the same, just like flipping the coin.
Now say you draw a club and put that card aside, instead of reshuffling it into the deck. What is the probability of drawing another club? In this scenario, the probability is going to change because our data has changed. Instead of there being 13 clubs left in the deck, there are now only 12. The total number of outcomes has also changed, dropping to 51. To calculate the probability, take the likelihood of drawing a club, 12, over the total number of outcomes, 51. Your answer is 12:51. That answer can't be reduced, because you can't divide 51 by 12.

Calculating probabilty is a simple matter of knowing the variables. Always check your final answer to see if it can be reduced by dividing the numbers into each other, or by a common factor.