Geometric Random Variables Part 1 A fair coin is flipped repeatedly until tails shows. What is...
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...
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?
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.
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.)
A fair coin is flipped until the first head appears. Let X= the total number of times the coin is flipped. Find E(x). Hint:if the first flip is tails, this "game" restarts.
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...
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)
tails up? 42. Juan draws a black card from an ordinary deck as the first card for a game of Gin Rummy. What is the probability the card was a king? What's the probability that the next black card is also a king given that the first one was? 43. At a carnival gambling booth, two dice are rolled, and a sum of 7 wins double your money. Find the probability that the sum is 7 given that one of...
We flip a fair coin until we get the 3-rd Head. What is the probability that we get exactly 6 Tails?
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...