Answer
Let $Δt$ be any interval.
1) $\lim\limits_{Δt \to 0} P(two~or~more~successes)=0$
2) If $Δt_1=Δt_2$ then $P(success~in~Δt_1)=P(success~in~Δt_2)$
3) Let $x_1$ be the number of successes in $Δt_1$ and $x_2$ be the number of successes in $Δt_2$. Given $Δt_1∩Δt_2=Ø$, $P(x_2~|~x_1)=P(x_2)$
Work Step by Step
Given above.
