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Suppose that we bet on the outcomes of coin flips in the following way 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). Each of us chooses a different series of three flips, and we flip a coin until three consecutive flips, in order, match your.

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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 What is the expected value of the number of flips we will take What is the probability that heads never occurs twice in a row

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Your proposed answer of $13/32$ is correct.

A coin is flipped eight times where each flip comes up either heads or tails How many possible outcomes a) are there in total B) contain exactly three heads C) contain at least three heads

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 The probability of a coin landing heads ten times in a row is.0009765625

There are 7,000,000 people on the planet

Each person can flip a coin 17280 times a day If every person on the planet flips coins until one person gets ten heads in a row, how long will it take to get the 10 heads in a row? 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.

If i get a tail on the first flip, the expected number of flips until i get a head is 2 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. 35 suppose we flip a coin until we see a head