Probability Trees and Calculations PDF

## Why are probability trees used? * To visualize multiple scenarios and follow successive steps where conditional probabilities are involved. ## Why are probabilities multiplied in certain cases? * Because the events are independent and we are trying to find the probability of their intersectio...

## Why are probability trees used? * To visualize multiple scenarios and follow successive steps where conditional probabilities are involved. ## Why are probabilities multiplied in certain cases? * Because the events are independent and we are trying to find the probability of their intersection. ## When is conditional probability used? * When we calculate the probability of an event knowing that another event has already occurred. ## When are probabilities added for certain events? * When the events are incompatible, meaning they cannot occur simultaneously and the probability of their union is the sum of their individual probabilities. ## What is an independent event? * An event that does not affect the probability of another event, meaning their probabilities do not change each other. ## When is Bayes' theorem used? * When $P(A|B)$ is known, and $P(B|A)$ needs to be calculated. ## What is total probability, and when is it calculated? * Total probability is calculated when an event can occur in multiple ways, and we need to find the probability of the event itself. ## What is an incompatible event? * Two events that cannot happen simultaneously, implying their intersection probability is 0. ## Why is division used in certain probability calculations? * To adjust a conditional probability based on new information. ## When does the probability of the union require subtraction? * When the events have a common intersection.