I have tried my best in solving this out for you.
DO UPVOTE! In case of any doubt, feel free to write in the comment
section below.
Flipping Coins For a fair coin, the chance of getting tails is 1/2. Counting the number...
Flipping Coins For a fair coin, the chance of getting tails is 1/2. Counting the number of tails Let's experiment with the total number of tails in n trials. Total number of tails in a small number of coin flips ם Suppose we flip 10 coins (with 1 = Tails and 0 = Heads). Here are six samples of size 10. = 10 trials = 6 for (i in 1: trials) { print (sample(c(0, 1), 1, replace=TRUE)) مه ## [1]...
Fraction of tails Now let's look at the fraction of tails in n trials. Fraction of tails in a small number of coin flips Heads) Suppose we flip 10 coins and compute the fraction of tails (with 1 = Tails and 0 = = 10 trials = 6 for (i in 1: trials) { print (sum(sample(c(0, 1), n, replace-TRUE)) /n) ## [1] 0.1 ## [1] 0.4 ## [1] 0.4 ## (1) 0.5 ## [1] 0.7 *# (1) 0.6 The expected...
Fraction of tails Now let's look at the fraction of tails in n trials. Fraction of tails in a small number of coin flips Tails and 0 = Heads). n Suppose we Aip 10 coins and compute the fraction of tails (with 1 = - 10 trials - 6 for (i in 1: trials) { print (sun (sample(c(0, 1), n, replace=TRUE)) / n) 3 ## (1) 0.1 ## (1) 0.4 ## [1] 0.4 ## [1] 0.5 ## (1) 0.7 ##...
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?
Rosencrantz and Guildenstern are flipping coins. Guildenstern has a bag with 100 coins in it. All of them are fair coins, except for 10 that each have heads on both sides and 2 that each have tails on both sides. Guildenstern reaches into the bag without looking, removes a randomly chosen coin, with each of the 100 coins equally likely, and flips it. Give exact answers expressed as simplified fractions. (a) What is the probability that it is one of...
2. Mysterioso the Magician is walking down the street with a box containing 25 identical looking coins: 24 are fair coins (which flip heads with probabilty 0.5 and tails with probability 0.5) and one is a trick coin which always flips heads. Renata the Fox skillfully robs Mysterioso of one of the coins in his box (chosen uniformly at random). She decides she will flip the coin k times to test if it is the trick coin (a) What is...
Suppose we flip a fair coin n times. We say that the sequence is balanced when there are equal number of heads and tails. For example, if we flip the coin 10 times and the results are HT HHT HT T HH, then this sequence balanced 2 times, i.e. at position 2 and position 8 (after the second and eighth flips). In terms of n, what is the expected number of times the sequence is balanced within n flips?
There are two coins, one fair and one biased (the probability of obtained a tails being 0.2 - i.e., P[T] = 0:2). A game is played by successively flipping the coins as follows: The game begins with a flip of the fair coin, and the result, H or T, is noted; If the result of the flip is T, then the other coin is used on the next flip, and the result is noted; If the result of a flip...
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.......
Question 2 Suppose you have a fair coin (a coin is considered fair if there is an equal probability of being heads or tails after a flip). In other words, each coin flip i follows an independent Bernoulli distribution X Ber(1/2). Define the random variable X, as: i if coin flip i results in heads 10 if coin flip i results in tails a. Suppose you flip the coin n = 10 times. Define the number of heads you observe...