Curious Probability

a) The probability that a positive integer is not a prime number is equal to $\displaystyle A = 1 - \lim_{n \to \infty} \frac{\frac{n}{\log (n)}}{n} = 1 - \lim_{n \to \infty} \frac{1}{\log (n)} = 1 - 0 = 1$

b) WLOG , we can suposse that 2 points are (0,0) and (1,0). Then it's sufficient that the third point is in the semiplane $x < 0$ or in the semiplane $x > 1$ and it is not in the line $y = 0$ ,for the 3 points forming an obtuse triangle. Therefore, the probability $B$ is bigger or equal to $4 \cdot \frac{1}{4} = 1 \Rightarrow B = 1$ .