3 possible outcomes. All equally likely? Some more likely than others? What's the max and min probability?
- Some probabilities are easy to understand and calculate. Even odds across the board. What are the odds of flipping a coin and getting heads? One in two, 50%. What are the odds of rolling a six sided die and getting a four? The odds are one in six. The nice thing about these two examples is that each possible outcome is equally as likely. By that I mean, the odds of getting heads is 50%, the odds of getting tails is 50%.
The odds of rolling any of these outcomes with the six sided die are equal. The odds of getting any one of these outcomes is one in six. It's not quite as easy to calculate the probability of a rainy day in Los Angeles tomorrow. It's not like we can say that the odds of rain tomorrow is 50% and the odds of no rain are 50%. In Los Angeles, typically there are only about 20 to 30 days per year when it rains.
And in London, there are typically over 100 days per year when it rains. In these cases we say that the odds are weighted. The odds that it might rain on any given day in Los Angeles is about 7%, and about 29% in London. Then again, we also need to remember that these probabilities are stated on the basis of an entire year. If I instead say, what are the odds that it will rain on December 10th in London? The probability of rain on that particular day may be much higher since December is traditionally London's wettest month.
That said, the sum of the probabilities of all possible outcomes must add up to 100%. So for our coin, 50% heads, 50% tails, 100% total. For our six sided die, each of our six outcomes has a probability of one in six. When we add up all six outcomes our probability is 1.0 or 100% So if we define each day as either a day with rain or a day without rain, in London the probability of rain on any given day might be stated as 29%.
So the probability of a dry day must be 71%. That again, sums up to 100%. Let's consider a scenario where I put two, red ping pong balls in a container. That's it, there is nothing else in the container. What are the odds that if you take one ball out of the container that it will be red? Obviously, since both balls in the container are red, the ball you take out of the container must be red. So the probability is 100%.
On the other hand, what are the odds that the ball you take out of the container will be white? There are no white balls in the container, so the odds are 0%. This outcome is not possible. These are both simple scenarios, but they help us understand a few basic things. The highest probability for any scenario is 100%. The lowest probability for any scenario is 0%. So, to recap, the probability of all possible outcomes must sum to 100%.
Sometimes the probability of every possible outcome is equally as likely. Sometimes some outcomes are more likely than others. But no matter what, the probability of an outcome can never be less than 0%, nor can it be greater than 100%.
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.