Suppose you have a coin and you gain $10 if you flip it and get a head and lose $10 if it is tail. What is the maximum theoretical range of you losses/ gains?
The range of profit is from -10 to +10$ as if one gts head one wins and get 10$ profit and if one gets tails there is a loss of 10$(profit of -10$)
Note that heads and tails are two only possible outcomes of the trail. We have assumed here that one tosses the coin only one time.
Suppose you have a coin and you gain $10 if you flip it and get a...
Problem 4: You flip a fair coin three times. Each time you get a head, you win S2. Each time you get a tail, you lose $1. What is your expected winning from this game?
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}
Suppose you can place a bet in the following game. You flip a fair coin (50-50 chance it lands heads). If it lands heads, you get 4 dollars, if it lands tails, you pay 1 dollar. This is the only bet you can make. If you don't make the bet you will neither gain nor lose money. What is the utility for you of the coin landing tails if you make the bet (assume utility is dollars)?
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?
Suppose you toss an unfair coin 8 times independently. The probability ofgetting a head is 0.3. Denote the outcome to be 1 if you get a head and 0 if a tail. (i) Write down the sample space Ω. (ii) What is the probability of the event that you get a head or a tail at least once? (iii) If you get eight same toss's you will get x dollars, otherwise you will lose 1 dollar. On average, how large...
Suppose you can place a bet in the following game. You flip a fair coin (50-50 chance it lands heads). If it lands heads, you get 4 dollars, if it lands tails, you pay 1 dollar. This is the only bet you can make. If you don't make the bet you will neither gain nor lose money. Should you place the bet?
You have a biased coin where heads come up with probability 2/3
and tails come up with probability 1/3.
2. Assume that you flip the coin until you get three heads or one tail. (a) Draw the possibility tree. (b) What is the average number of flips? Use the possibility tree, and show your calculation.
2. Assume that you flip the coin until you get three heads or one tail. (a) Draw the possibility tree. (b) What is the average...
Suppose you have two coins. One coin is fair and other is a coin with heads on both sides. Now you choose a coin at random and flip the coin. If the coin lands head, what is the probability that it was the fair coin?
Flip a coin twice and observe its face side. Assume that the coin is unfair with P(head)=0.6. Define the following events: •A: you get at least one head •B: you get at least one tail Write out sample space S, events A,B by listing all possible outcomes. (b) FindP(A), P(B) (c) FindP(A∪B),P(A∩B) (d) FindP(A|B) (e) Are A,B independent? and why?
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?