A total of 46 percent of the voters in a certain city...

A total of 46 percent of the voters in a certain city classify themselves as Independents, whereas 30 percent classify themselves as Liberals and 24 percent say that they are Conservatives. In a recent local election, 35 percent of the Independents, 62 percent of the Liberals, and 58 percent of the Conservatives voted. A voter is chosen at random. Given that this person voted in the local election, what is the probability that he or she is (a) an Independent? (b) a Liberal? (c) a Conservative? (d) What percent of voters participated in the local election?

A total of 46 percent of the voters in a certain city classify themselves as Independents, whereas 30 percent classify themselves as Liberals and 24 percent say that they are Conservatives. In a recent local election, 35 percent of the Independents, 62 percent of the Liberals, and 58 percent of the Conservatives voted. A voter is chosen at random. Given that this person voted in the local election, what is the probability that he or she is
(a) an Independent?
(b) a Liberal?
(c) a Conservative?
(d) What percent of voters participated in the local election?

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

Bayes' Theorem

Bayes' Theorem is used to update the probability estimate for an event based on new information. It relates the conditional probability of a cause given an observed outcome to the reverse, i.e., the probability of the outcome given that cause, and incorporates prior knowledge about the probability of the cause.

Population Partitioning

This concept involves dividing a total population into distinct, non-overlapping groups to analyze probabilities within these subgroups. It is particularly useful in determining overall probabilities and conditional probabilities when dealing with heterogeneous groups.

Conditional Probability

This concept concerns the probability of an event occurring given that another event has already occurred. It forms the basis for analyzing relationships between events in a probability space, particularly in cases where events are interdependent.

Law of Total Probability

This principle states that if a sample space is partitioned into several mutually exclusive events, then the probability of any event can be calculated by summing the probabilities of that event occurring within each partition, weighted by the probability of each partition. It is essential in problems where overall probabilities are determined by several conditional probabilities.

Transcript

Please give Ace some feedback