An event with a probability < 0.05 is considered to be an unusual event. The probability of getting n heads in a row is computed here as:
= 0.5*0.5*0.5.... n times
Therefore we compute n here as:
For n = 4, we have: 0.54 = 0.0625
For n = 5, we have: 0.55 = 0.03125 < 0.05
Therefore 5 heads in a row may make us conclude that the coin is biased, as the probability of that happening is less than 0.05.
How many heads in a row would it take until YOU thought the coin was biased?...
A biased coin is tossed until a head occurs. If the probability of heads on any given toss is .4, What is the probability that it will take 7 tosses until the first head occurs? The answer i got was , (.60)^2(.40) Now for the second part it says, what is the probability that it will take 9 tosses until the second head occurs. Is the answer for this part be 9C2(.40)^2(.60)^7 or 8C1(.40)(.60)^5 I can't figure out if its...
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 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?
A coin is biased such that the probability of flipping heads is .2. If the coin is tossed 15 times, what is the probability of getting exactly 5 heads?
9.74. Suppose we toss a biased coin independently until we get two heads or two tails in total. The coin produces a head with probability p on any toss. 1. What is the sample space of this experiment? 2. What is the probability function? 3. What is the probability that the experiment stops with two heads?
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....
Suppose you just flipped a fair coin 8 times in a row and you got heads each time! What is the probability that the next coin flip will result in a heads? Write answer as a decimal and round to 1 place after the decimal point.
Suppose you flip a fair coin repeatedly until you see a Heads followed by another Heads or a Tails followed by another Tails (i.e. until you see the pattern HH or TT). (a)What is the expected number of flips you need to make? (b)Suppose you repeat the above with a weighted coin that has probability of landing Heads equal to p.Show that the expected number of flips you need is 2+p(1−p)/1−p(1−p)
Flip four biased coin at the same time, and denote the total number of heads by X. If those four coins have 0.3,0.4,0.7,0.8 probability to land heads: E(X) V(x)
1. A fair coin is flipped until three heads are observed in a row. Let denote the number of trials in this experiment. [This is a simple model of some procedures in acceptance control]. b) Find p(x) for the first five values of X c) Make an estimate of EX. Hint: use geometric rv related to X.