A fair coin is repeatedly flipped. The following sequence of
heads and tails comes up: HTTHTHHTHHHHH.
What is the probability that the next result will be a head?
1/64 |
|
1/32 |
|
1/2 |
|
1/14 |
A fair coin is repeatedly flipped. The following sequence of heads and tails comes up: HTTHTHHTHHHHH....
Stacy and George are playing the heads or tails game with a fair coin. The coin is flipped repeatedly until either the fifth heads or the fifth tails appears. If the fifth heads occurs first, Stacy wins the game. Otherwise, George is the winner. Suppose that after the fifth flip, three heads and two tails have occurred. What is the probability that Stacy wins this game?
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.
A coin that comes up heads with probability p is flipped n consecutive times. What is the probability that starting with the first flip there are always more heads than tails that have appeared?
4. A fair two-sided coin is tossed repeatedly. (a) Find the expected number of tails until the first head is flipped. (b) Find the probability that there are exactly 5 heads in the first 10 flips. (c) Use the central limit theorem/normal approximation to approximate the probability that in the first 100 flips, between 45 and 55 of the flips are heads.
Answer part a and part b
please!!!
(a) What is the conditional probability that exactly four Tails appear w when a fair coin is flipped six times, given that the first flip came up Heads? (I.e. the coin , then is flipped five more times with Tails appearing exactly lour times.) (b) What if the coin is biased so that the probability of landing Heads is 1/3? (Hint: The binomial distribution might be helpful here.)
(a) What is the conditional...
6. A fair coin is flipped repeatedly until 50 heads are observed. What is the probability that at least 80 flips are necessary? (You may calculate an approximate answer.)
Problem 2: Tails and (Heads or Tails?) Alice and Bob play a coin-tossing game. A fair coin (that is a coin with equal probability of 1. The coin lands 'tails-tails' (that is, a tails is immediately followed by a tails) for the first 2. The coin lands 'tails-heads (that is, a tails is immediately followed by a heads) for the landing heads and tails) is tossed repeatedly until one of the following happens time. In this case Alice wins. first...
Problem 2. A coin results in head with probability 1/3. This coin is repeatedly flipped independently. Find the probability that at most five flips are necessary to find four flips that result in tails.
Geometric Random Variables Part 1 A fair coin is flipped repeatedly until tails shows. What is the probability of the game stopping on exactly the 5 th flip? What is the probability of the game stopping on one of the first 5 flips? Part 2 Cards are drawn with replacement from a standard shuffled deck repeatedly until a black 10 appears. What is the probability of the game stopping on exactly the 15th card? What is the probability of the...
Geometric Random Variables Part 1 A fair coin is flipped repeatedly until tails shows. What is the probability of the game stopping on exactly the 5 th flip? What is the probability of the game stopping on one of the first 5 flips? Part 2 Cards are drawn with replacement from a standard shuffled deck repeatedly until a black 10 appears. What is the probability of the game stopping on exactly the 15th card? What is the probability of the...