If the probability function of a random variable $X$ is given by $P(X=n)=\frac{k(n+1)}{3 n}$ for $n \in \mathbf{N} \cup\{0\}$ where $k$ is a constant, then $P(X<2)=$

An observer counts 240 vehicles per hour at a specific location on a highway. Assuming that the arrival of vehicles at the location follows Poisson distribution, the probability that more than two vehicles arrive over a 30 sec time interval is

If the roots of each of the equations $2 x^2+x-1=0$, $3 x^2-10 x+3=0$ and $6 x^2+11 x-2=0$ corresponds to probabilities of three events of a random experiment, then those events are

Cards are drawn one after the other without replacement from a well shuffled pack of cards until and ace card appears. If the probability that exactly 5 cards are drawn before the first ace card appears is $\frac{4}{49}\left(\frac{p_1 \cdot p_2 \cdot p_3}{p_4 \cdot p_5 \cdot p_6}\right),\left(p_i\right.$ is prime, $\left.i=1,2,3,4,5,6\right)$ then $\left(\max \left\{p_i\right\}-\min \left\{p_i\right\}\right)=$