In this video we discuss the basic concepts, types and rules of probability in statistics and also cover the key terms used in probability. We go through probability examples to help gain a basic understanding of probability. Transcript/notes
Probability basic concepts
Rolling a die, drawing a card out of a deck and flipping a coin are all things we are familiar with, and these are often used to discuss the basic concepts of probability.
There are 4 key terms that are often used with probability, a probability experiment, which is a process where specific results are obtained, such as rolling a die, as there are only 6 possible outcomes.
And outcome is another key term, which is a single result of a probability experiment, so, if you draw a 4 of hearts from a full deck of cards, that is an outcome.
Sample space is another key term, and it is the set of all possible outcomes for a probability experiment. For instance, the sample space for rolling 2 dice is here, you can see the possible outcomes for die 1 and the possible outcomes for die number 2, and the sample space is the pairs of numbers listed on the chart here, so, there are 36 possible outcomes in this sample space.
Event is another key term used in probability, and an event is the set of outcomes of a probability experiment, it is a subset of the sample space, and an event with one outcome is a simple event, and a compound event consists of 2 or more outcomes. For instance, the event of rolling a 4 on a die roll is a simple event, and the event of getting an even number on a die roll is a compound event.
There are 3 main types of probability, classical probability, empirical probability, and subjective probability.
Classical probability is used when each outcome in a sample space is equally likely to occur, for instance the sample space for rolling 2 dice, and each of these outcomes has the same chance to occur. The formula for this is P of E, probability of any event equals number of outcomes in event E divided by the total number of outcomes in the sample space. So the probability of the 2 dice totaling 5 is P of 5 equals 4 divided by 36, the total number of outcomes in the sample space.
Empirical probability is when each outcome is not equally likely to occur and it is based on observations obtained from experiments. For instance, lets say you polled 50 people and asked them what their favorite sport is. Using a frequency table, 29 said football, 11 said basketball, 6 said baseball, 3 said soccer, and 1 said tennis. Now we can compute probabilities for each of the categories.
The formula for empirical probability is probability of event equals frequency for the class or the event, divided by the total of the frequencies. So the probability of football being a person’s favorite sport is 29 divided by 50, which is 0.58, and the probability of tennis being someone’s favorite sport is 1 divided by 50, which is 0.02. And you can convert these to percentages by multiplying by 100 to get 58% and 2%.
Subjective probability is based on an educated guess or an estimate. If I were to say there is a 73% chance the Yankees win the World Series next year, this is based on my experience and evaluation.
And there are 4 key rules to probability. The first is that the probability of any event is between 0 and 1, including 0 and 1, and this is written as 0 less than or equal to probability of an event, less than or equal to 1.
And whatever the value of P is, can be written as a fraction or a decimal. For instance, the probability of getting a head on a coin toss is 0.5, or 1 over 2.
Rule number 2 is the total sum of all possible outcomes in a sample space is 1. So, the sample space for a die roll is 1 through 6, with each having a 1 over 6 probability of occurring, add these up and we get 1.
Rule number 3 is if it is impossible for a given event to occur, so it is not part of the sample space, its probability is zero. For instance the probability of rolling a 8 on a die roll is not part of the sample space, so its probability is zero.
Rule number 4 is that if an event is certain to occur, its probability is 1. So, the probability of rolling a 1 through a 6 on a die roll is certain to happen, so its probability is 1.
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