Suppose you toss a coin (heads or tails) three times. The prior probability of the hypothesis H that the coin is double-headed (you always get heads) is P(H) = 1/5, while the prior probability of the hypothesis ¬H that it is not double-headed (i.e. it is fair) is P(¬H) = 4/5. If you get three heads in the three tosses (evidence E), what is the posterior (updated) probability of the hypothesis P(H | E) that the coin is double-headed?

Suppose you toss a coin (heads or tails) three times. The prior probability of the hypothesis H that the coin is double-headed (you always get heads) is P(H) = 1/5, while the prior probability of the hypothesis ¬H that it is not double-headed (i.e. it is fair) is P(¬H) = 4/5. If you get three heads in the three tosses (evidence E), what is the posterior (updated) probability of the hypothesis P(H | E) that the coin is double-headed?

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

Age Age Gender Under 40 40 or Older Total Male 12 2 14 Female 8 3 11 Total 20 5 25 The table above shows the distribution of age and gender for 25 people who entered a contest. If the contest winner will be selected at random, what is the probability that the winner will be either a female or 40 or older? 13/25 16/25 3/25 10/25
Use the given probability value to determine whether the sample results could easily occur by chance, then form a conclusion. A study of 420,095 cell phone users resulted in 135 who developed cancer of the brain or nervous system. When comparing this sample group to another group of people who did not use cell phones, it was found that there is a probability of 0.512 of getting such sample results by chance. What do you conclude? The probability shows that the sample results ▼ could could not have easily occurred by chance. It appears that there ▼ is not is sufficient evidence to conclude that cell phones have an effect on cancer of the brain or nervous system.
4-If P (A U B) = 0.64 and Event A and B are mutually exclusive, which of the following could be possible probabilities for A and B? A) P(A) = 0.8, P(B) = 0.8 B) P(A) = 0.42, P(B) = 0.22 C) P(A)=0.8, P(B)=0.16 5-In how many ways can distinct permutations are there of the letters in the word "statistics"? (A) 50400 (B) 50200 (C) 50000 [15 marks]
All freshmen students must take Intro to Business and Business Communications in their first semester. 45% of the freshmen students get assigned to Prof. Abernathy's Intro to Business Class, and 50% of students get assigned to Prof. Bertrand's BComm class. (You can presume that being assigned to one class is independent of your being assigned to the other.) What is the probability that someone has Abernathy for Intro, but not Bertrand for BComm Question 2 There's a glitch in ChatRoulette, and it matches you with a completely random person, despite your request to be matched with someone of a particular gender. Suppose that 80% of ChatRoulette participants are men (20% are women); 70% of participants are bat-shit crazy (30% are sane); and the proportion of crazies is the same regardless of gender. What is the probability that your next match is a sane man? Question 3 Freshmen are sometimes assigned to first-year sections at random. Suppose that the probability that your…
A student decided to blindly guess at every question on a multiple-choice test with 20 questions (please do not do this!). The probability that they guess an individual question correct is 0.25 because each question has four options. What is the probability that they get at least 25% score on the test? That is: what is the probability that they get at least 5 of the 20 questions correct? 0.9961 0.4148 0.0031 0.6172 0.2023 0.5852
We know that the probability of Taylor Swift dying her hair bright pink is .50. Given that she has dyed her hair pink there is a 40% chance that she is complaining about an ex-boyfriend. a.) Write down the information given in terms of the probabilities of event C (Taylor Swift dyes her hair pink) and event D (she is complaining about an ex-boyfriend). b.) What is the probability that Taylor Swift is not complaining about an ex-boyfriend and she dyed her hair pink (hint: think about using the conditional probability you’re given here)? c.)What is the probability that Taylor Swift is not complaining about an ex-boyfriend and she did not dye her hair pink (hint: can you use independence here)? d.) Knowing Taylor Swift is not complaining about an ex-boyfriend, what is the probability that she did not dye her hair pink?
At a gas station, 40% of customers use regular gasoline, 35% use extra gasoline and the remaining ask for premium gasoline. Of those who consume regular gasoline, only 30% fill the tank, of those who buy extra, 60% fill the tank and those who carry premium, 50% fill the tank. If the next customer fills the tank, the probability that he asks for premium gas is:
In the Introduction to Impossibility module, 4/5 of students pass the exam. Of those who pass the exam 9/10 attend lectures, and of those who fail only 1/2 attend lectures. What is the probability that a student who doesn’t attend lectures passes the exam?
A class in advanced physics is comprised of 20 juniors, 30 seniors and 10 graduate students. The final grades showed that 5 of the juniors, 12 of the seniors, and 6 of the graduate students received an A for the course. If a student from this class is selected and is found to have earned an A, what is the probability that he or she is a junior? Ans is Blank 1 (round off your final answer into four decimal places. #.####)
Consider the experiment: You ask someone two multiple-choice questions. Each question could be answered with Yes (Y), No (N), or Don't Know (D). (For example, if you ask someone these two questions, they could answer Yes to both of them, or Yes to the first one and Don't Know to the second one, etc.) Let A be the event that the person answers Yes to at least one question, and Let B be the event that the person answers No to the second question. How many elements are in the sample space? What elements are in A ∩ B? What elements are in A ′?
The probability that a person who identifies as male will be color-blind is 0.036. Find the probabilities that in a group of 54 people who identify as male, the following will be true. (a) Exactly 5 are color-blind. (b) No more than 5 are color-blind. (c) At least 1 is color-blind.
A large store has a customer service department where customers can go to ask for help with store-related issues. According to store records, approximately 4 of customers who go to the service department ask for help finding an item. Assume the reason each customer goes to the service department is independent from customer to customer. Based on the approximation, what is the probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item? 4(1) 1 – (¹)¹ 1-()* 4(4)'()* Q000