Joint, Marginal, and Conditional Probabilities

Joint Probability

• Intersectiion

It occurs whenever event A and event B both occur

• Joint Probability

The probability that the intersection of two events occurs

• "A and B",

• Example
  

Marginal probability

• Marginal probability

The probability that an individual event from one experiment occurs, regardless of the outcomes from another experiment

• Example

  
  

Conditional probability

• Conditional probability

When one event occurs, it may impact the probability of an event from a different experiment

• Definition

The probability that a second event(B) will occur given that we know that the first event(A) has already occurred

• A and B come from two different experiments
  vertical bar "|" means "given"

• Formula
  
  B Event we want the probability for
  A Event that has already occurred

  • Find the joint probability of A and B
  • Find the marginal probability of the event that has already occurred(Event A)
  • Divide te joint probability by the marginal probability

Main take away

• Joint probability indicates the intersection portion, which both event A and event B occur at the same
• Marginal probability represents the probability of one event reguardless the outcomes from other events
• Conditional probability yields the probability of event B with reguard the event A has already happened.