Dec 29, 2023 · Two players, A and B, alternatively toss a fair coin (A goes first, then B). The game ends when there is a head followed by a tail (HT), and the person who tosses the tail wins. What is the probability that A wins?

The problem can be mapped on a one-dimensional discrete random walk.Imagine that you start at 0 and you make a step +1 (for the outcome HT) with probability $1/4$, a step -1 (for the outcome TH) with probability $1/4$, and a step 0 (for the outcomes TT and HH) with probability $1/2$.

Apr 5, 2018 · Two people decided to play a coin toss game. The rules of the game are: (i) Everyone plays 2 times in sequence; (ii) the first to obtain two head wins; Suppose that the two individuals names are A and B. A starts play the game and throw a coin twice times and after that B throw the coin twice and so on, the first obtain two head in sequence wins.

May 15, 2024 · Since the coin is fair, the probability of getting heads or tails is 0.5. However, I'm not sure how to apply this concept when the coin is flipped until both heads and tails have appeared. For part (b), I'm a bit confused. My initial thought was that since the coin is fair, the probability that the last flip lands on heads would be 0.5.

For instance, HHT indicates that the coin landed with a head up on the first two tosses and a tail up on the third. a) List all the possible outcomes of the sample space. b) Write each of the following events as a set and find its probability.

Feb 15, 2020 · A fair coin is flipped n times. Let X be the number of times that the outcome is head. What is the smallest value of n for which the given inequality is satisfied? $0.99 ≤ P(0.49 ≤ \frac{X}{n}≤ 0.51)$ Ok so, I tried to consider the random variable of the result of a coin toss as a uniform distribution in which 1 is heads and 0 is tails.

Jan 9, 2019 · Coin toss problem, get exactly 2 heads in 5 tosses. 2. Coin toss bias estimation problem. 1. Probability ...

The current problem has a fair coin, and asks that the coin be tossed until a particular pattern, HTHT, shows up, and then asks what is the probability that another pattern, TTH, actually occurs before HTHT shows up. Think of this problem as a two-player game again: the coin is tossed, until either HTHT or TTH show up.

Jun 16, 2019 · a coin toss and a die roll simultaneously Hot Network Questions When flying a great circle route, does the pilot have to continuously "turn the plane" to stay on the arc?

I'm not sure that you wrote out the explanation of the question correctly (please correct me if I'm wrong), but if you bet S, then right after betting and before the coin is tossed your wealth is x-S.. now if the game is such that you either lose everything or gain 2S, then your wealth after one coin toss is either x-S or x-S+2S=x+S with prob ...