Flip four biased coin at the same time, and denote the total number of heads by...
You have a biased coin, where the probability of flipping a heads is 70%. You flip once, and the coin comes up tails. What is the expected number of flips from that point (so counting that as flip #0) until the number of heads flipped in total equals the number of tails?
Problem 4. Five coins are flipped. The first four coins will land on heads with probability 1/4. The fifth coin is a fair coin. Assume that the results of the flips are independent. Let X be the total number of heads that result Hint: Condition on the last flip. (a) Find P(X2) (b) Determine E[X] S.20
(1 point) Consider a game played by flipping biased coins where the probability of heads is 0.14. You first choose the number of coins you want to flip You must pay $1.5 for each coin you choose to flip. You flip all the coins at the same time. You win $1000 if one or more coins comes up heads How many coins should you flip to maximize your expected profit? Answer: What is your maximum expected profit? Answer: $ (Your...
Suppose that you flip five fair coins and roll three fair dices at the same time and all the events are independent. (a) What is the probability that exactly two coins land heads up and one dice shows a six? (b) What is the probability that at least four coins land heads up and two dices show a number less than three? (c) What is the probability that the total number of heads is an even-number and the addition of...
Suppose C1;C2;C3 are three didifferent biased coins, whose probability of heads equals 0.4, 0.5, and 0.2 respectively. Suppose coins are placed together in a box and you randomly picked a coin from the box. Flip the coin 10 times. Let A denote the event you randomly chose coin C1. Let B denote the event that you got exactly 4 heads out of the 10 coin flips. Compute the following probabilities: P(A∩B) P(B) P(A|B)
If you flip a coin and roll a die at the same time, what is the probability of rolling a 5 or 6 and the coin showing heads? Question 3 Unanswered If you flip a coin and roll a die at the same time, what is the probability of rolling a 5 or 6 and the coin showing heads? (answer to 4 decimal places) Type your response
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...
You suspect that a coin is biased such that the probability heads is flipped (instead of tails) is 52%. You flip the coin 51 times and observe that 31 of the coin flips are heads. The random variable you are investigating is defined as X = 1 for heads and X = 0 for tails, and you wish to perform a "Z-score" test to test the null hypothesis that H0: u = 0.52 vs. the alternative hypothesis Ha: u > 0.52....
4. Toss a fair coin 6 times and let X denote the number of heads that appear. Compute P(X ≤ 4). If the coin has probability p of landing heads, compute P(X ≤ 3) 4. Toss a fair coin 6 times and let X denote the number of heads that appear. Compute P(X 4). If the coin has probability p of landing heads, compute P(X < 3).
Problem 1. A biased coin with probability plandin with a Heads is lipped 4 times. (a) Define the basic random variables and give the sample space and assign probabilities to the outcomes. (b) Let X be the total number of Heads in the four flips Draw a Venn diagrain showing the five events X = ii 0,1,2,3,4 as well as the sample space and the outcomes. Is X a random variable? c) Are the events X 1 and X 2...