**Coin Flip Probability Problem**1. **What is the probability that the flip lands on heads?**2. **Given that the flip lands on heads, what is the probability that you picked one of the fair coins?**---In this problem, you're asked to determine the probability of a coin flip resulting in heads and then, given this outcome, the probability of having selected one of the fair coins. This involves understanding concepts of probability, including conditional probability, which assesses the likelihood of an event occurring, given that another event has already occurred. Say you have three coins in your pocket. Two of the coins are fair coins (have a head side and a tail side, and each side is equally likely), and you have one coin that both sides are heads. Label the fair coins C₁ and C₂, while the unfair two-headed coin is labeled as C₃.You are going to reach into the pocket and randomly pick a coin (each coin has 1/3 chance of being picked), and then you are going to flip that coin.Given that the flip lands on heads, what is the probability that you picked the two-headed coin?

Answered: Say you have three coins in your…

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...

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Suppose I flip a fair coin n = 20 times. A psychic tries to predict the outcome before each flip. Three researchers have different ideas about the psychic's ability. There is Sydney, the Skeptic (S), who thinks the psychic's success rate is between 49% and 51%. There is Morgan, the Mark, M, who thinks that the psychic's success rate is 80%. And there is Carter, the Cynic (C), who thinks the psychic's success rate is 10%. Specifically: S+ 0 ~ U(.49, .51) M + 0 = .80 C0 = .10 %3D In all cases, assume the number of successful predictions follows a binomial distribution with success rate 0. Usek for the number of successes and n for the number of trials. Given all that: Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Carter over Morgan. Call that Bayes factor Bc:M Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Morgan over Sydney. Call that Bayes factor BM:S Determine the formula for the Bayes factor (a.k.a., likelihood…
Wendy needs to get to an airport from a hotel. There is 0.33 chance that she calls a cab, there is 0.11 chance that she gets a Uber. If she cannot get a cab or Uber, she will take a shuttle. If she calls a cab, there is 0.29 chance that she could miss the flight. If she gets a Uber, the chance of missing flight is 0.22. If she takes the shuttle, the chance is 0.28. What is the probability that she misses the flight? (Round your answer to three decimal places)
A student is taking an exam and doesn't know the answers to 3 of the questions, so they decide to guess randomly on all three of them. One of the questions is a true/false question, one is a multiple choice question with 3 possible answers, and one is a multiple choice question with 4 possible answers. What is the percentage chance that they will answer all 3 questions correctly?
The chess club needs to nominate a government (president, vice president, treasurer, and secretary). What are the chances I could be the president of the club if there are 31 other members (32 total)?
A vending machine contains 1000 lollipops. Some of the lollipops are red, and the others are blue. You don’t know how many there are of each color. However, you do know that these two alternatives are equally likely. There are 900 blue lollipops and 100 red ones. There are 500 blue lollipops and 500 red ones. When you put a coin into the vending machine, it gives you a lollipop, chosen at random. Suppose that it gives you a blue lollipop. What is the probability that there are 900 blue lollipops and 100 red ones? Show how you got the answer.
likely to get 19. Shreya conducted a study to see if name-brand flashlight batteries last longer than gencric batteries, on avcrage. For each of 20 flashlights, she flipped a coin. If it was heads shc uscd namc-brand batteries and if it was tails she used the generic brand. She left the flashlights on and recorded how long it took for the batterics to wear out. The results showed that the flashlights that had the name-brand batteries, on average, lasted significantly longer than the flashlights that used the generic brand. What type of design is this study? a. This study is an example of a simple random sample. b. This study is an example of a matched pairs experiment. This study is an example of a completely randomized experiment. This study is an example of an obscrvational study. c. d.
A coffee shop has a "manager surprise" drink that randomly chooses among 4 drinks. If Lee goes to the coffee shop for 3 days, what are the odds Lee would have been given the same drink all 3 days?
There are two bags A and B. Bag A contains n white balls and 2 black balls while bag B contains 2 white balls and n black balls. One of the two bags is selected at random and two balls are drawn from it without replacement. We know that if both the balls drawn are white balls, the probability of bag A being selected to draw the balls is . Find the value of n.
A lock consists of 3 dials, where each dial has 4 letters. What is the probability of guessing the right combination in one try? Kay has an 80% probability of making a free-throw in basketball, and each free-throw is independent. Kay gets to take 2 free-throws and must make both to win the game. What is the probability that Kay's team will win the game? Two owners of a cattle ranch, Jo and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows: Jo weighs 25 cows and gets an average weight of 1,350 pounds (stdev 50) Val weighs 100 cows and gets an average weight of 1,420 pounds (stdev 50) What is Jo’s margin of error, rounded to the nearest whole number? (The formula is )
Directions: Solve the given problem. Show your solutions. Of all the registered automobiles in Colorado, 8% fail the state emissions test. Twelve automobiles are elected at random to undergo an emissions test. a. Find the probability that exactly four of them fail the test. b. Find the probability that fewer than four of them fail the test. c. Find the probability that more than three of them fail the test.
Suppose you’re on a game show like Let’s Make A Deal and there are 4 doors to choose from. There are 3 mules and one car behind the four doors. Once you choose your door, the host will open one of the doors with a mule. This means that there are 3 unopened doors left, 2 with mules and 1 with the car. What is the probability of winning the car if you stick to your original choice? What is the probability if you switch to one of the other unopened doors? Explain your answer

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