The probability of winning a lotter is $0.01$. How many times do you need to play to win with probability at least $0.6$? Assume that lottery draws are statistically independent.

My failed attempt:

Let $P(W)=0.01\\P(L)=0.99$

and let $X$ be the number of wins.

Then the event $\{X=k\}$ follows a binomial distribution. So we calculate how many trials are needed for the probability of the former event to be equal to at least $0.6$:

$P(X=k) = \binom{n}{k}(0.01)^k(0.99)^{n-k}=0.6$

I should now solve for $n$.

Is this the correct approach?