Appliance Reliability Companies A, B, and C produce 15%,...

Appliance Reliability Companies A, B, and C produce 15%, 40%, and 45%, respectively, of the major appliances sold in a certain area. In that area, 1% of the company A appliances, of the company B appliances, and 2% of the company C appliances need service within the first year. Suppose a defective appliance is chosen at random; find the probabilities that it was manufactured by the following companies. Company A

Appliance Reliability Companies A, B, and C produce 15%, 40%, and 45%, respectively, of the major appliances sold in a certain area. In that area, 1% of the company A appliances,
of the company B appliances, and 2% of the company C appliances need service within the first year. Suppose a defective appliance is chosen at random; find the probabilities that it was manufactured by the following companies.

Company A

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Conditional Probability

Conditional probability refers to the likelihood of an event occurring given that another event has already occurred. In problems like these, it is used to determine the probability that an appliance comes from a specific company given that it was found to be defective.

Law of Total Probability

The Law of Total Probability provides a way to compute the overall probability of a given event by considering all the possible ways that event can occur. In this context, it is used to calculate the overall defect rate by summing the individual defect probabilities from each company, weighted by their production shares.

Bayes' Theorem

Bayes' Theorem is a fundamental principle in probability theory that is used to update the probability of a hypothesis as new evidence becomes available. In the problem, it helps to determine the probability that a defective appliance was made by a particular company by relating the known overall defect rates and the specific company's defect probability.

Transcript

Please give Ace some feedback