how many times must a man toss a fair coin, so that the probability of having at least one head - Maths - Probability

Question

how many times must a man toss a fair coin, so that the
probability of having at least one head is more than 80%
???????

Ajanta Trivedi · Accepted Answer

let he toss the coin n times the probability of getting only heads = $(\frac{1}{2})^{n}$ the probability of getting only tails = $(\frac{1}{2})^{n}$ the probability of getting atleast one head = $1 - (\frac{1}{2})^{n}$ according to the question: $1 - (\frac{1}{2})^{n} > \frac{80}{100} 1 - (\frac{1}{2})^{n} > \frac{4}{5} (\frac{1}{2})^{n} < 1 - \frac{4}{5} (\frac{1}{2})^{n} < \frac{1}{5} \Rightarrow 2^{n} > 5 n > 2$ therefore he must toss the coin 3 times

how many times must a man toss a fair coin, so that the probability of having at least one head is more than 80% ???????