Two numbers are selected at random ( without replacement ) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find the probability distribution of the random variable X, and hence find the mean of the distribution.

Question

$(a)\;\large\frac{17}{3} \qquad(b)\;\large\frac{14}{3}\qquad(c)\;\large\frac{15}{2}\qquad(d)\;\large\frac{17}{5}$