Calculating the population size given a probability

Question

I'm not too sure how to even start this question. Could someone explain how to solve this question :)

Question: The minimum number of times that a fair coin can be tossed so that the probability of obtaining a head on each trial is less than 0.0005 is?

I tried using binomial distribution formula (the one with nCr) by setting the population as n, p=0.5 and x; however, this didn't work at all. Could someone help :)

Answer 1

The number of heads in $n$ trials is indeed $X\sim Bin(n,p)$. The probability of only heads is $\Pr(X=n)=p^n$ which should be less than $0.0005$. Setting $p=0.5$ we get $0.5^n<0.0005$ which is true starting from $n=11$.

Answer 2

Set the inequality

$$0.5^n<0.0005$$

and solve with respect to n obtaining

$$n\geq 11$$