Conditional Probability

DEFINITION of 'Conditional Probability'

Probability of an event or outcome based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding event.

BREAKING DOWN 'Conditional Probability'

Conditional probabilities are contingent on a previous result. For example, suppose you are drawing three marbles - red, blue and green - from a bag. Each marble has an equal chance of being drawn. What is the conditional probability of drawing the red marble after already drawing the blue one? First, the probability of drawing a blue marble is about 33% because it is one possible outcome out of three. Assuming this first event occurs, there will be two marbles remaining, with each having a 50% of being drawn. So, the chance of drawing a blue marble after already drawing a red marble would be about 16.5% (33% x 50%).