What is probability? The most basic probability calculations. What might that number mean?
- What are the chances I can flip a coin and get heads three times in a row? What's the likelihood a certain basketball player will make a free throw? What are the odds that it will rain in Berlin tomorrow? What are the chances a child born today will live to be 90 years old? Everyone is interested in probability. Science, sports, business, gambling, all of them rely on probability in an effort to make informed decisions.
But, what is probability? I guess the most basic definition would be the likelihood that some event will occur. Typically it's measured via a ratio. The desired outcome divided by all possible outcomes. So let's go back to my very first question. What are the chances I can flip a coin and get heads three times in a row? So, we have a random experiment: tossing a coin.
The sample space, which is a list of all the possible outcomes is this. As you can see, we have eight possible outcomes. Only one of those is the desired outcome. So, you can see the probability of getting heads three times in a row is one in eight, or 12.5%. Let's try one more. This time, we can roll a pair of dice. What are the odds I will roll two sixes? Our random experiment, rolling a pair of dice.
The sample space is given here. So this time we have 36 possible outcomes. Only one of those is the desired outcome. Our probability of rolling double sixes is one in 36, or about 2.8%. Dice and coins are easy though. They tend to be fair, and thus, fairly predictable. Most of life doesn't work that way, though. It's not always easy quantify all the possible outcomes.
For example, what are the odds your boss will wear a black dress to work tomorrow? It would depend on who your boss is, how many black dresses they have, how many other outfits they might own. Perhaps, we also need to understand the events of that work day. Some of the things we might know. Some we would not know. Maybe only some of those things are important. Perhaps, there are other factors we have not even considered.
The formula for basic probability may be simple, but that doesn't mean calculating probability is easy. Let's also consider this scenario. Let's say, you and I bet. I tell you, that so long as you do not roll a double six with two dice, you will win the bet. You have a 97.2% chance of winning. Suppose you roll the dice, and you roll a double six, does this mean the probability was wrong? No, it simply means you were every unlucky.
Probability does not guarantee an outcome. It simply tries to inform you on the possibilities. Next time someone provides you with a probability consider how it was calculated, whether or not you trust the probability, and what the number actually means. Understanding probability, both its strengths and its weaknesses, definitely increases your odds of making good decisions.
Professor Eddie Davila covers statistics basics, like calculating averages, medians, modes, and standard deviations. He shows how to use probability and distribution curves to inform decisions, and how to detect false positives and misleading data. Each concept is covered in simple language, with detailed examples that show how statistics are used in real-world scenarios from the worlds of business, sports, education, entertainment, and more. These techniques will help you understand your data, prove theories, and save time, money, and other valuable resources—all by understanding the numbers.
- Calculate mean and median for specific data sets.
- Explain how the mode is used to assess a data set.
- Identify situations in which standard deviation can be used to investigate individual data points.
- Use mean and standard deviation to find the Z-score for a data point.
- List the three different categories of probability.
- Analyze data to determine if two events are dependent or independent.
- Predict possible outcomes for a situation using basic permutation calculations.
- Give examples of binomial random variables.