4. [4] Let $p$ be the answer to this question. If a point is chosen uniformly at random from the square bounded by $x=0, x=1, y=0$, and $y=1$, what is the probability that at least one of its coordinates is greater than $p$ ?
Answer: $\square$
The probability that a randomly chosen point has both coordinates less than $p$ is $p^{2}$, so the probability that at least one of its coordinates is greater than $p$ is $1-p^{2}$. Since $p$ is the answer to this question, we have $1-p^{2}=p$, and the only solution of $p$ in the interval $[0,1]$ is $\frac{\sqrt{5}-1}{2}$.