A student owns two types of six-sided dice. The first type are normal fair dice, which land on each side with probability 16 . The second type are biased dice that land as a six with probability 0.5 and the other five sides with probability 0.1 each. The student’ sprior belief is there is a 20% chance the dice he is holding is a biased dice, and an 80%chance the dice is a fair dice. The student rolls the dice twice and gets two sixes. What now is his posterior belief that the dice is biased

A student owns two types of six-sided dice. The first type are normal fair dice, which land on each side with probability 16 . The second type are biased dice that land as a six with probability 0.5 and the other five sides with probability 0.1 each. The student’ sprior belief is there is a 20% chance the dice he is holding is a biased dice, and an 80%chance the dice is a fair dice. The student rolls the dice twice and gets two sixes. What now is his posterior belief that the dice is biased

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

A faite dice is tossed twice Find the Probability that the two faces are the same CLEAR
At the Washington University 35%, 25% and 40% of the students in Calculus are taught by Prof. A, Prof. B and Prof. C, respectively. The respective probabilities of failing in Calculus for the three professors are 6%, 7% and 5%. A student in Calculus in the previous semester was randomly selected and was found out to have failed in the subject. Under which class most likely did he belong?
An experiment is rolling two fair dice. What is the probability that the sum is 6?
Ponderosa Paint and Glass carries three brands of paint. A customer wants to buy another gallon of paint to match paint she purchased at the store previously. She can’t recall the brand name and does not wish to return home to find the old can of paint. So, she selects two of the three brands of paint at random and buys them. What is the probability that she matched the paint brand? Her husband also goes to the paint store and fails to remember what brand to buy. So, he also purchases two of the three brands of paint at random. Determine the probability that both the woman and her husband fail to get the correct brand of paint. (Hint: Are the husband’s selections independent of the wife’s selections?)
Two fair dice are rolled. What is the probability the first die has an even number and the second die has a 6?
At a local restaurant, you are allowed to pick one side with your dinner. Because you can only choose one, your side choice is mutually exclusive of all the other sides to chose from. On any given day, there is a 0.34 chance you will pick an fries, and a 0.1 chance you will pick an veggies. Today, you do not pick an veggies; what is the probability you pick fries today?
A shop keeper sells three models of televisions A, B and C.Sale of model A is 40% of which 3% are with stereo.Sale of model B is 40% of which 7% are with stereo.Sale of model C is 20% of which 9% are with stereo.What is the probability that a randomly sold television is with stereo?
A company requires all job applicants to undergo drug testing for employment. If the applicant has used drugs the test has a 90% chance of a positive result. If the applicant has not used drugs the test has an 85% chance of a negative result. 4% of all applicants have used drugs. If an applicant has a positive test, what is the probability he or she has actually used drugs?
The probability that a trainee will remain with a company is 0.6. the probability that am employee earnsbmore than k10,000 per month is 0.5. the probability that an employee who is a trainee remained with the company or who earns more than k10,000 per month is 0.7. what is the probability that an employee earns more than k10,000 per month given that he is a trainee who stayed with the company
Samatya supermarket is planning to order souvenir cups for the upcoming national feast. The cups cost $5 and sells for $20 each. The managers believe that the demand will be 500 cups with 20% probability, 1000 cups with 50% probability and 1500 cups with 30% probability. They plan to order 600, 1000 or 1300 cups. They have the opportunity to order 200 cups more for with a $15 per cup cost if the demand comes out as 1500 cups. The cups left on hand will be scrapped as there will be no more demand for them. Draw and solve the decision tree for this problem.
In the experiment of rolling two unloaded dice. What is the probability that the sum of the two dice is 2?