There are four main characteristics of a geometric experiment. The following are additional attributes of the geometric distribution: Formally: P(x=n+k|x≥k+1)=P(x=n),Px=n+k|x≥k+1=P(x=n), where k = number of previous failures Jones’s probability of a hit begins anew each time he comes to bat. This feature…
A more valuable probability density function with many applications is the binomial distribution. This distribution will compute probabilities for any binomial process. A binomial process, often called a Bernoulli process after the first person to fully develop its properties, is…
The simplest probability density function is the hypergeometric. This is the most basic one because it is created by combining our knowledge of probabilities from Venn diagrams, the addition and multiplication rules, and the combinatorial counting formula. To find the…
Figure 4.1 You can use probability and discrete random variables to calculate the likelihood of lightning striking the ground five times during a half-hour thunderstorm. (credit: modification of work “CG lightning strike” by Axel Rouvin/ Flickr, CC BY 2.0) A student takes…
Terminology In this module we learned the basic terminology of probability. The set of all possible outcomes of an experiment is called the sample space. Events are subsets of the sample space, and they are assigned a probability that is…
A Venn diagram is a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample space S together with circles or ovals. The circles or ovals represent events. Venn diagrams also help us to…
Contingency Tables A contingency table provides a way of portraying data that can facilitate calculating probabilities. The table helps in determining conditional probabilities quite easily. The table displays sample values in relation to two different variables that may be dependent or contingent…
When calculating probability, there are two rules to consider when determining if two events are independent or dependent and if they are mutually exclusive or not. The Multiplication Rule If A and B are two events defined on a sample space, then: P(A∩B)=P(B)P(A|B)P(A∩B)=P(B)P(A|B). We can think…
Independent and mutually exclusive do not mean the same thing. Independent Events Two events are independent if one of the following are true: Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. For example, the outcomes…
Probability is a measure that is associated with how certain we are of outcomes of a particular experiment or activity. An experiment is a planned operation carried out under controlled conditions. If the result is not predetermined, then the experiment is said…