The probability that the card is a king is 4 divided by 52, which equals 1/13 or approximately 7.69%. Now, suppose it is revealed that the selected card is a face card.

The probability the selected card is a king, given it is a face card, is 4 divided by 12, or approximately 33.3%, as there are 12 face cards in a deck.

Lesson 9 presents the conjugate model for exponentially distributed data. Posterior probability is the revised probability of an event occurring after taking into consideration new information.

Posterior probability is calculated by updating the prior probability by using Bayes' theorem.

The formula can also be used to see how the probability of an event occurring is affected by hypothetical new information, supposing the new information will turn out to be true.

For instance, say a single card is drawn from a complete deck of 52 cards.

This module introduces concepts of statistical inference from both frequentist and Bayesian perspectives.

Lesson 4 takes the frequentist view, demonstrating maximum likelihood estimation and confidence intervals for binomial data.

Prior probability, in Bayesian statistical inference, is the probability of an event before new data is collected.

This is the best rational assessment of the probability of an outcome based on the current knowledge before an experiment is performed.

For example, a simple probability question may ask: "What is the probability of Amazon.com, Inc., (NYSE: AMZN) stock price falling?

" Conditional probability takes this question a step further by asking: "What is the probability of AMZN stock price falling If A is: "AMZN price falls" then P(AMZN) is the probability that AMZN falls; and B is: "DJIA is already down," and P(DJIA) is the probability that the DJIA fell; then the conditional probability expression reads as "the probability that AMZN drops given a DJIA decline is equal to the probability that AMZN price declines and DJIA declines over the probability of a decrease in the DJIA index. This is also the same as the probability of A occurring multiplied by the probability that B occurs given that A occurrs, expressed as P(AMZN) x P(DJIA|AMZN).

Bayes' theorem, named after 18th-century British mathematician Thomas Bayes, is a mathematical formula for determining conditional probability.

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