Um A has 5 white and 7 black balls. Urn B has 3 white and 12 black balls. We flip a fair coin. I

Name: Problem 34, Chapter 3: A First Course in Probability
Uploaded: 2022-01-22T14:19:03-08:00
Duration: 2 min 5 s
Channel: Wendi Zhao
Description: Um A has 5 white and 7 black balls. Urn B has 3 white and 12 black balls. We flip a fair coin. If the outcome is heads, then a ball from urn A is selected, whereas if the outcome is tails, then a ball from urn B is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails?

step 1 We want to compute the conditional probability that the ball is chosen from um b, given that it

Question

Um $A$ has 5 white and 7 black balls. $\operatorname{Urn} B$ has 3 white and 12 black balls. We flip a fair coin. If the outcome is heads, then a ball from urn $A$ is selected, whereas if the outcome is tails, then a ball from urn $B$ is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails?

   Um $A$ has 5 white and 7 black balls. $\operatorname{Urn} B$ has 3 white and 12 black balls. We flip a fair coin. If the outcome is heads, then a ball from urn $A$ is selected, whereas if the outcome is tails, then a ball from urn $B$ is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails?

A First Course in Probability

Sheldon M. Ross 5th Edition

Chapter 3, Problem 34

Instant Answer

Solved by Expert Wendi Zhao

01/22/2022

Step 1

According to the formula of conditional probability, this is equal to the probability that the ball is chosen from urn B and it is white, divided by the probability that the ball is white. Show more…

Show all steps

Thanks for your feedback!

Um $A$ has 5 white and 7 black balls. $\operatorname{Urn} B$ has 3 white and 12 black balls. We flip a fair coin. If the outcome is heads, then a ball from urn $A$ is selected, whereas if the outcome is tails, then a ball from urn $B$ is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails?

Play audio

Feedback

Wendi Zhao and 61 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

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 provides a mathematical framework for updating prior beliefs based on new evidence. It calculates the probability of a cause given an observed event by relating the conditional probabilities and the marginal probabilities of the events involved.

Law of Total Probability

The law of total probability breaks down the probability of an event into a sum of conditional probabilities over a complete set of mutually exclusive scenarios. It is essential when dealing with situations where an event can occur in multiple ways, each with its own probability.

Conditional Probability

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is crucial when updating probabilities based on new information, such as determining the probability of one outcome given the observed result of another.

Please give Ace some feedback