Belchfire Motors automobiles are equally likely to be...

Belchfire Motors automobiles are equally likely to be manufactured on Monday, Tuesday, Wednesday, Thursday, or Friday; no cars are constructed on weekends. Ralph Wader, the company statistician, has determined that 4 percent of the cars produced on Monday are "lemons"; 1 percent of the cars made on Tuesday, Wednesday, or Thursday are lemons; and 2 percent of cars manufactured on Friday are lemons. You find that your Belchfire car is truly a lemon. What is the probability it was manufactured on Monday?

Key Concepts

Uniform Distribution

A uniform distribution refers to a probability distribution where all outcomes are equally likely. In this context, each day (Monday through Friday) is assumed to have the same chance of production unless otherwise stated, making it a key concept for determining base probabilities in the analysis.

Conditional Probability

Conditional probability is the probability of an event occurring given that another event has already occurred. This concept is crucial when determining the probability of the car being from a specific day given that the car is a lemon, as it focuses on the likelihood based on the provided conditions.

Bayes' Theorem

Bayes' Theorem is a fundamental principle used to update probabilities based on new evidence. It relates the conditional and marginal probabilities of random events and is applied here to reverse conditional probabilities—calculating the probability the car was manufactured on a specific day given that it is a lemon.

Law of Total Probability

The law of total probability states that the total probability of an event is the sum of the probabilities of that event occurring under each mutually exclusive scenario. In this scenario, it is used to compute the overall probability of a car being a lemon by summing up the contributions from each day of production.

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