Question

You allow your friend, Sally, to shuffle a three-card deck consisting of an ace, a king, and a queen. Sally chooses two of the cards at random and discards the third. She shows you a queen when you ask for a picture card. What is the probability that she also has the king?

Name: Problem 70, Chapter 2: Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition (Computer Science and Scientific Computing)
Uploaded: 2021-06-11T21:43:47-08:00
Duration: 2 min 7 s
Channel: J Hardin
Description: You allow your friend, Sally, to shuffle a three-card deck consisting of an ace, a king, and a queen. Sally chooses two of the cards at random and discards the third. She shows you a queen when you ask for a picture card. What is the probability that she also has the king?

   You allow your friend, Sally, to shuffle a three-card deck consisting of an ace, a king, and a queen. Sally chooses two of the cards at random and discards the third. She shows you a queen when you ask for a picture card. What is the probability that she also has the king?

Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition (Computer Science and Scientific Computing)

Arnold O. Allen 2nd Edition

Chapter 2, Problem 70

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Solved by Expert J Hardin

06/11/2021

Step 1

The possible pairs she could pick are: - Ace and King (AK) - Ace and Queen (AQ) - King and Queen (KQ) Show more…

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You allow your friend, Sally, to shuffle a three-card deck consisting of an ace, a king, and a queen. Sally chooses two of the cards at random and discards the third. She shows you a queen when you ask for a picture card. What is the probability that she also has the king?

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Key Concepts

Conditional Probability

This concept involves finding the probability of an event occurring given that another event has already occurred. It adjusts the likelihood based on the additional information provided, allowing for better-informed probability assessments in scenarios with known outcomes.

Sample Space Analysis

This involves enumerating all possible outcomes of a random process and identifying the events of interest. In probability problems, organizing the complete set of equally likely outcomes is essential for calculating the likelihood of various events when new information is introduced.

Bayesian Reasoning

This is a method for updating probabilities based on new evidence. By applying Bayes’ rule, one can re-evaluate the probability of an event (such as holding a specific card) in light of observed outcomes, enhancing decision making under uncertainty.

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