The probability of observing HHH after flipping a fair coin three times equals 0.125 or 12.5...
Question is are X and Y independent? Why? 1. Consider flipping a fair coin three times and observe whether it lands heads up or tails up. Let X the number of switches from either head to tail or vice versa. For example, when THT is observed, the number of switches is 2 and when HHH is observed, the number of switches is 0. Also, let Y be the number of tails shown in the three times of flipping.
1. Consider flipping a fair coin three times and observe whether it lands heads up or tails up. Let X the number of switches from either head to tail or vice versa. For example, when THT is observed, the number of switches is 2 and when HHH is observed, the number of switches is 0. Also, let Y be the number of tails shown in the three times of fipping. (a) List all the values of the joint probability mass...
Probability Puzzle 3: Flipping Coins If you flip a coin 3 times, the probability of getting any sequence is identical (1/8). There are 8 possible sequences: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT Let's make this situation a little more interesting. Suppose two players are playing each other. Each player choses a sequence, and then they start flipping a coin until they get one of the two sequences. We have a long sequence that looks something like this: HHTTHTTHTHTTHHTHT.......
If we flip a fair coin 15 times, what is the probability of not flipping 15 heads in a row?
Suppose a fair coin is tossed 4 times. What is the probability of flipping exactly 3 heads?
In flipping a coin 12 times and observing heads or tails, how many different outcomes can be obtained?
A fair coin is flipped 20 times. a. Determine the probability that the coin comes up tails exactly 15 times. b. Find the probability that the coin comes up tails at least 15 times. c. Find the mean and standard deviation for the random variable X giving the number of tails in this coin flipping problem.
11. What are the possible combination outcomes when you toss a fair coin three times? (6.25 points) H = Head, T = Tail a {HHH, TTT) Ob. (HHH, TTT, HTH, THT) c. {HHH, TTT, HTH, THT, HHT, TTH, THH) d. (HHH, TTT, HTH, THT, HHT, TTH, THH, HTT} e. None of these 12. What is the probability of you getting three heads straight for tossing a fair coin three times? (6.25 points) a. 1/2 OD. 1/4 C. 118 d. 1/16...
Suppose that prior to conducting a coin-flipping experiment, we suspect that the coin is fair. How many times would we have to flip the coin in order to obtain a 96.5% confidence interval of width of at most .12 for the probability of flipping a head? (note that the z-score was rounded to three decimal places in the calculation) a) 309 b) 226 c) 229 d) 312 e) 306 f) None of the above
Problem 7) True/False 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. True/False: In this problem, the random variable X is considered as a...