Probability Equations: Determining the Odds

probability equationsWhat is the probability that you are going to read through this entire outline?  Well, the answer could depend on a number of factors: how much time you have, if you are tired or not, or, whether or not your friends are going to sit and study along with you.  Given those three factors, you can determine the probability of whether or not you will read through the entire outline by factoring in the possible outcomes.  How interesting, (or intrusive – depending on how you look at it), is that?

Probability determines the chance and likelihood that something will occur.  There are specific equations that go along with probability formula structures that you can use to determine these outcomes.  Today, we are going to take a look at some examples of basic equations that are used in probability.  So, if you determined that you are not tired and you are going to read on, get out your pencil and paper and let’s get started!

Why is Probability Important?

Before we get into some necessary equations for probability, you might be asking yourself: why is probability important?  There is a good chance that you had your share of learning probability in grade school, high school, and possibly in college – so why keep at it?

  • Likelihood:  Nothing in life is certain aside from death and taxes, right?  Probability is here to help us determine the likelihood of everything else.  Sure, we may not know if a certain drug is going to cause harm to our bodies, but we can definitely factor in probability to help us come up with possible outcomes of a situation.
  • Decision Making:  When you know the likelihood that an event or outcome can happen, the more informed and researched your decision can be.  This can be used in work, school, and regular day to day life.
  • Fun:  Probability can be fun when you apply it to actual events, because as you watch instances play out, you will be able to determine the truth behind the numbers on paper.  Also, we are sure you can name a few Game Shows off the top of your head that use probability as well!

Probability of an Event

Let’s get started with one of the more basic equations using the formula for the probability of an event.  We are going to start with the formula:

(A) =The Number Of Ways Event A Can Occur
The total number Of Possible Outcomes

Example:  You are given a single six-sided di.  What is the probability of rolling each outcome?

Answer:  The equation for rolling a 1 will be:

P(1) =# of ways to roll a 1 =1
total # of sides6

You will be able to apply this same type of equation to come up with the probability for each outcome.  Here is one more example, say, if you want to figure out what the probability of rolling a 5 will be:

P(5) =# of ways to roll a 5 =1
total # of sides6

 Probability of A Single Random Event

Let’s say that now you want to calculate the probability that a single random event will occur.

Example:  A jar contains 3 blue marbles, 6 red marbles, and 11 white marbles.  You are going to draw a marble from the jar at random.  What is the probability that the marble that you draw is going to be red?

Answer:  The equation that you will use here is 6/20 = .30 = 30%.  Here is a little explanation: the number of events is six because there are six red marbles that are in question.  The number of outcomes would be 20, because that is the total number of marbles that you have altogether.  Therefore, the probability is 6 ÷ 20 = 3/10 or .30 or 30%.

Probability of Multiple Random Events

Let’s use the same example with the jar of marbles that we used above.

Example:  A jar contains 3 blue marbles, 6 red marbles, and 11 white marbles.  You are going to draw three marbles from the jar at random.  What is the probability that the first marble is red, the second marble is blue, and the third marble is white.

Answer:  The probability that the first marble is red is will be shown in the equation 6/20, or 1/4.  This is because you are starting with all your 20 marbles.  The probability that the second marble is blue will be expressed in the equation 3/19.  You will use 19 because you now have one fewer marble after your first draw, but not one fewer blue marble.  Lastly, the probability that the third marble is white will be 11/18, because you have already drawn two marbles, bringing the total count down to 18.

Converting Odds to Probability

Say you want to determine the odds that something is going to happen—you can do this with probability as well!

Example:  Determine the likelihood that the turtle is going to win the race.  The odds are expressed in the equation 10:4.  The 10 in the equation represents the likelihood that the turtle will win, and the 4 represents the probability that the turtle will lose.

Answer:  We are going to use the equation 10+4 to determine the total number of outcomes that are possible.  This gives us 14.  We are going to take the 10 representing the probability that the turtle will win, and divide that by the total number of outcomes possible.  This is expressed in the equation: 10/14 = 0.7142 or 71.42%. So, the probability that the turtle will win the race is 71.42%.

What is the Probability?

There you have it!  If you have gone this far, you have made it through the entirety of this outline.  Hopefully, you were able to previously determine the correct probability of you getting this far.  Remember, that probability can be fun and applied to all aspects and areas of life.  Keep the general rules and formulas of probability in mind as you are writing your equations, and you will be well on your way to finding out the truth behind the numbers!