Problem 4: You flip a fair coin three times. Each time you get a head, you...
Imagine an experiment where we flip a coin 6 times, and get “head, tail, head, head, head, head”. Which of the following statements are true? a) The coin is not fair b) The coin’s tail probability is 1/6 c) The sequence "head, tail, head, head, head, head" is an outcome in the sample space. d) The sample space of the experiment is {head, tail}
5. You play a game using an unfair coin. Suppose that each time the coin is tossed, the probability of showing "head" is 1/3 and the probability of showing "tail" is 2/3. Also suppose that each time the coin shows head you win 10 dollars and you lose 3 dollars when it shows tail. How much money do you expect to win when the coin is tossed 10 times?
Step 1. Flip a fair coin. Step 2. If you got a head in step 1, flip two fair coins. If you got a tail in step 1, flip one fair coin. Given that you got only tails in step 2, what is the chance that you got tails in step 17 Round your answer to nearest.xx
Suppose that a fair coin is tossed ten times. Each time it lands heads you win a dollar, and each time it lands tails you lose a dollar. Calculate the probability that your total winnings at the end of this game total two dollars, and the probability that your total winnings total negative two dollars.
You flip a coin four times and observe whether a head or a tail occurs on each flip. How many outcomes are in the sample space for this random phenomenon?
An unfair coin is flipped. If a head turns up, you win $1. If a tail turns up, you lose $1. The probability of a head is .61 and the probability of a tail is .39 Let X be the random variable for the amount won on a single play of this game. What is the expected value of the game?
Problem 3. You play a game where you first choose a positive integer flip a fair coinn times. You win a prize if you get exactly 2 heads. How should you choose n to maximize your chance of winning? What is the chance if winning with optimal choice of n? There are two equally good choices for the best n. Find both n and then an
Q1 Q2 Q3 Step 1. Flip a fair coin. Step 2. If you got a head in step 1, flip two fair coins. If you got a tail in step 1, flip one fair coin. Given that you got only tails in step 2. what is the chance that you got tails in step 1? Round your answer to nearest .xx Five people roll a 60-sided die which has labels 1, 2, ..., 60. What is the chance that all...
An unfair coin is flipped. If a head turns up, you win $1. If a tail turns up, you lose $1. The probability of a head is.36 and the probability of a tail is .64. Let X be the random variable for the amount won on a single play of this game. What is the expected value of the game? E(X)= dollars (Type an integer or a decimal. Round to the nearest cent as needed.)
QUESTION 8 Problem 8) A fair coin is tossed 20 times. A fair coin means that the probability of getting a head is the same as the probability of getting a tail. Let X be the number of coins of getting head. Note that there are only two possible outcomes: getting head or tail after tossing the coin. X follows a binomial distribution with n=20, p=0.5. Answer the following questions. (Question) Find the expected value of X, E(X). QUESTION 9...