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1 there are two possibilities for each of the five tosses of the coin, so there are $2^5 = 32$ possible outcomes in your sample space, as you found I know that the expected value of flipping the coin once i. What is the probability that heads never occurs twice in a row

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Your proposed answer of $13/32$ is correct. What is the expected value if you flip the coin 1000 times If i get a tail on the first flip, the expected number of flips until i get a head is 2

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This is because, after getting a tail, the coin is fair and the probability of getting a head on the next flip is 0.5

Therefore, on average, it would take 2 flips to get a head. Suppose you flip a fair coin repeatedly until you see a heads followed by a tails What is the expected number of coin flips you have to flip By manipulating an equation based on the result of the f.

35 suppose we flip a coin until we see a head What is the expected value of the number of flips we will take I am pretty new to expected value, so i tried to evaluate it by multiplying the probability of each scenario with the number of flips it took to get there (like taking the arithmetic mean). A participant is allowed to ask 1 yes or no question (e.g

Was the first coin flip heads?), then plays a game where he tries to guess all 100 coins

The participant is awarded $\$1$ for every coin guessed correctly, and loses $\$1$ for each incorrect guess. Assume that you are flipping a fair coin, i.e Probability of heads or tails is equal Then the expected number of coin flips required to obtain two consecutive heads for the first time is

(a)4 (b)3 (c)6 (d)10 (e)5 i worked up like let n be the number of tosses required untill 2 consecutive heads are obtained for the first time. A sees a tail on coin flip 2 and 4 so he picks 3, b does the same After running this on a computer simulation i get a 60% winrate Although i don't fully understand why

A 70% chance of winning has been found on my puzzling stackexchange duplicate post

Strategies so far 70% chance of winning by @jaap scherphuis Two players alternately flip a coin What is the probability of winning by getting a head Ask question asked 13 years, 10 months ago modified 3 years, 1 month ago

If you get heads you win \\$2 if you get tails you lose \\$1