Chapter 3 4 Bayes Probabilites Bayes Probability Questions

Chapter 3 -4 Bayes Probabilites

Bayes Probability Questions which involve conditional probabilities are very common in applications of probability theory, and one type of conditional probability is so common that is has a special name. Use tree diagrams and formulas to compute probabilities.

Example 1 Marvin’s Music places 80% of special orders for CDs to a distributor in Los Angeles and the remainder to a distributor in New York. Special orders are always shipped “next day delivery” by the distributor, but they do not always arrive the next day. Shipments from Los Angeles are late 5% of the time, and shipments to New York are late 10% of the time. If a randomly selected special order arrives on time, what is the probability that it came from Los Angeles?

Example 2 Clyde has a rather casual attitude toward his courses, and he studies for 1/3 of his exams selected at random. In the past he has passed three-fourths of the exams he has studied for, and one-fourth of those he has not studied. Clyde passed his math exam. Find the probability that he studied for it.

Bayes Theorem

Example 3 A faculty member at GSU regularly teacher an evening course in a neighboring city. Each time he makes the trip he is randomly assigned transportation from the university motor pool. The motor pool consists of 50% chevys, 30% Fords, and 20% Volkswagens. Some of the cars are air-conditioned, others are not: 60% of the Chevys are air-conditioned, 50% of the Fords, and 30% of the Volkswagens. One afternoon, the faculty member is assigned an airconditioned car. What is the probability that it is a Chevy?

Example 4 A bucket labeled H contains 3 yellow and 2 white balls, and a bucket labeled T contains 2 yellow and 1 white ball. An experiment consists of flipping a coin once, and according to which side comes up, selecting 2 balls in succession and without replacement from the bucket labeled H (if heads) or T (if tails). The color of each ball is noted as it is drawn. W is white, Y is yellow. 1. If exactly one white ball is drawn, what is the probability that the coin landed with a head up? 2. If the second ball drawn is white, what is the probability that the coin landed with a head up?