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How many times do you need to toss a fair coin to get $100$ heads with probability $90$%?
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112 times check it I may be wrong. .

let number of tosses be N. probability of head=1/2, probability of tail=1/2

using binomial distribution, let X be a random variable. X denotes number of heads

$P(X=100)=\binom{N}{100}*0.5^{N-100}*(1-0.5)^{100}$=0.9
by Loyal (5.2k points)