What is the probability of a coin landing on heads 8 times in a row flipping it 100 times?
To find the probability of a coin landing on heads 8 times in a row when flipping it 100 times, we need to use the binomial probability formula.
The formula for the probability of getting exactly r successes (heads in this case) in n trials (flips in this case) with a probability of success (landing on heads) p, is given by:
P(X = r) = (nCr) * (p^r) * ((1-p)^(n-r))
In this case, r = 8 (getting heads 8 times in a row), n = 100 (flipping the coin 100 times), and p = 0.5 (probability of landing on heads for a fair coin).
Using the formula, let's calculate the probability:
P(X = 8) = (100C8) * (0.5^8) * ((1-0.5)^(100-8))
Using a calculator or spreadsheet software, we can evaluate this expression:
P(X = 8) ≈ 0.0214
Therefore, the probability of a coin landing on heads 8 times in a row when flipping it 100 times is approximately 0.0214 or 2.14%.