Basic probability concepts in statistics

Introduction to probability distribution and probability formulas

Probability definitions and formulas

  1. Classical Probability Method: The theoretical probability can be calculated if all outcomes are equally likely.  To calculate the theoretical probability
    1. Count the total number of possible outcomes
    2. Among the possible outcomes, count the number of ways an event can occur.
    3. Determine the probability as follows:

P(A) = Number of ways event A can occur/ total number of outcomes


Example:  what is the probability of drawing a 10 from a deck of cards? First we figure out how many number of outcomes there are. Since there are 52 cards then there are 52 possible outcomes. From those outcomes how many ways can we draw a 10, since there are four 10’s in a deck of cards then there are four ways we can draw a 10. Therefore the probability of drawing a 10 from a deck of cars is 4/52 which is .0769 or 8%.

  1. Relative Frequency Method: This method is used we approximate the probability an event will occur based on the relative frequencies counted from many observations.
    1. Repeat or observe a process many times and count the number of times the event of interest A occurs.
    2. Estimate P(A) by:

P(A)  = number of times A occurred / total number of observations

Example:  Suppose I observe that I observe that a basketball player has made 30 of her last 100 free throws which is 30%. The probability that she will make her next free throw is 30%.

  1. Subjective Probability: This is probability based on experience or intuition.

Example:  The probability that the next time I get in the elevators at work I will get stuck is 10%. This is based on my experience with the elevators at work.