Probability Distribution

In the world of statistics, we are introduced to the concept of probability. On page 146 of our text, it defines probability as “a value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur” (Lind, 2012). When we think about how much this concept pops up within our daily lives, we might be shocked to find the results. Oftentimes, we do not think in these terms, but imagine what the probability of us getting behind the wheel of a car twice a day, Monday through Friday, and arriving at work and home safely. Thankfully, the probability for me has been ‘one’! This means that up to this point I have made it to work and returned home every day without getting into an accident. While probability might have one outcome with one set of circumstances, this does not mean it will always turn out that way. Using the same example, just because I have arrived at work every day without getting into an accident, this does not mean it will always be true. As I confess with my words, and pray it does stay the same, probability tells me there is room for a different outcome.

In business, we often look at the probability of success or financial gain when making a decision. There are several things to take into consideration such as the experiment, potential outcomes, and possible events. An experiment is a process that leads to the occurrence of one and only one of several possible observations, while an outcome is a particular result of an experiment (Lind, 2012, p.146). An event is a collection of one or more outcomes of an experiment (Lind, 2012, p.147). There are three different types of probabilities that may be used in business decisions. The first is classical probability, which means that the outcomes of an experiment are equally likely. For example, say a business places an opening for job and the only requirement is the applicants are over the age of 18. Let’s assume four people applied, the probability of the oldest person getting selected is just as likely as one of the other three getting selected. There is nothing weighing the scales for one of the individuals any more than the next.

The second is empirical probability, which says the number of times an event happens is divided by the number of observations. Using the same scenario of the job opening, let’s assume now that although the only requirement is the applicants are over the age of 18, every time this company has a job opening they hire someone with a college degree. In this example, we would look at the number of times the company has hired an individual with a degree and divide that total number by the times the company has hired for the position.

Finally, the last type of probability is subjective, which is based on the likelihood of a particular event happening that is assigned by an individual based on whatever information is available. Again, we look at the company hiring for this position, but this time we observe that every time they make the requirements for the applicant to possess a degree, the number of skilled applicants nearly doubles. The company may then establish their decision on this available data and require all applicants to hold a degree. We can see from the three probabilities they are based on equally likely outcomes, relative frequencies, or available data.

With probability, we must also look at the distribution, which shows the possible outcomes of an experiment and the probability associated with each outcome (Lind, 2012, p.187). There are different types of random variables we can take into consideration which are broken into quantitative or qualitative values. Quantitative things have specific numbers attached to them, while qualitative things do not, making the variable of each experiment random. A discrete probability distribution can only have particular values, while continuous distributions can have a countless number of values in a range. Probability distributions are defined by the mean, variance and standard deviation. Each of these items has specific equations, where numbers can be attributed as a solution. The mean is a weighted average where the random variables are weighted according to the probability of occurrence (Lind, 2012, p.191). CWV

As humans, we have certain decisions we must make in regards to our beliefs. When deciding what religion to follow, many people ask themselves what the probability is that they will meet their maker. In Christianity, the Bible tells us in John 3 exactly how we can meet God and enter into His presence. Jesus says in verse three, “Very truly I tell you, no one can see the kingdom of God unless they are born again.” By accepting Jesus Christ as our Lord and Savior, we are promised that we will enter into the kingdom of God.

In essence, there is a probability of ‘one’ that we will meet our creator. We can say the same facts about people who will not inherit the kingdom of God. Galatians 5:19-21 says, “The acts of the flesh are obvious: sexual immorality, impurity and debauchery; idolatry and witchcraft; hatred, discord, jealousy, fits of rage, selfish ambition, dissensions, factions and envy; drunkenness, orgies, and the like. I warn you, as I did before, that those who live like this will not inherit the kingdom of God.” By this, we know the probability of these people not inheriting the kingdom of God is also ‘one’.

Finally, as we look at the Word of God and analyze the ultimate gift of sacrifice from God, we can see He sent His son Jesus to die for us. Sadly, much of the world is mistaken because they seem to think they can ‘earn’ their way into heaven by works or deeds. Ephesians 2:8-9 says, “For it is by grace you have been saved, through faith and this is not from yourselves, it is the gift of God not by works, so that no one can boast.” This tells us that the probability of getting into heaven is one, while people have misconstrued this truth with belief of ‘chance’ that we can earn our way into heaven. The reality is that Jesus is the only one way to the Father and the true ‘one’ true and absolute probability that we can enter into the kingdom of God.

References

Lind, Douglas A. (2012). STASTICAL TECHNIQUES IN BUSINESS & ECONOMICS. 1-844.