Conditional Probability
Definition
The probability of event A given that event B has already occurred, written P(A|B). Conditional probability is the basis of the multiplication rule in its general form and the foundation of the likelihood ratio framework used in evaluative forensic reporting. It is treated in depth in the next topic.
- Notation
- P(A|B), probability of A given B has occurred
- Underlies
- General multiplication rule
- Forensic application
- Foundation of the likelihood ratio framework
- Related concept
- Independence, where P(A|B) equals P(A)
Common questions
Why is conditional probability central to how forensic scientists report evidence strength?+
The likelihood ratio compares the conditional probability of the evidence given the prosecution proposition against the conditional probability of the same evidence given the defence proposition, letting an expert express how much the evidence favours one explanation over the other without stating a probability of guilt.
What is the prosecutor's fallacy and how does it involve conditional probability?+
It is the error of treating the probability of the evidence given innocence, P(evidence|innocent), as if it were the probability of innocence given the evidence, P(innocent|evidence), which are generally not the same value and confusing them can dramatically overstate the evidence's weight.
How does conditional probability differ from joint probability in practice?+
Joint probability, P(A and B), measures the chance both events occur together, while conditional probability measures the chance of A specifically within the subset of cases where B is already known to have occurred, and the two are linked by the multiplication rule.
Related terms
- Complement
- A group of heat-labile serum proteins (approximately 30 proteins, designated C1 through C9 in the classical pathway) that can be activated by...
- Event
- Any subset of the sample space to which a probability is assigned. An event may be a single outcome (this particular allele)...
- Hardy-Weinberg Equilibrium
- A condition in a population where genotype frequencies at a single locus conform to expectations derived from allele frequencies alone, assuming random...
- Independent Events
- Two events where the occurrence of one provides no information about the other: P(A and B) = P(A) x P(B). In forensic...
- Linkage Disequilibrium
- The non-random association of alleles at different loci within a population. Certain HLA allele combinations (e.g., HLA-A1 with HLA-B8 with HLA-DR3) occur...
- Multiplication Rule
- For any two events: P(A and B) = P(A) x P(B|A). When A and B are independent, this simplifies to P(A) x...
- Mutually Exclusive Events
- Two events that cannot both occur in the same trial. If a fibre is classified as cotton, it cannot simultaneously be classified...
- Positive Dependence
- Events are positively dependent when the occurrence of one increases the probability of the other: P(A|B) > P(A). In this case P(A...
- Sample Space
- The set of all possible outcomes of an experiment. In forensic genetics, the sample space for a single allele call is the...
- Statistical Independence
- Events A and B are independent if P(A|B) = P(A), equivalently P(A and B) = P(A) x P(B). Knowing B occurred gives...
Explained in these topics
- Basic Probability Rules
- Conditional Probability and IndependenceThe probability of event A given that event B has occurred, written P(A|B) = P(A and B) / P(B). It updates the probability of A in light of new information abo...