JEE Main 2010 — Probability & Statistics

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colour is

Four numbers are chosen at random (without replacement) from the set $\{1,2,3, \ldots ., 20\}$. Statement-1: The probability that the chosen numbers when arranged in some order will form an AP is $\frac{1}{85}$. Statement-2: If the four chosen numbers from an AP, then the set of all possible values of common difference is $\{\pm 1, \pm 2, \pm 3, \pm 4, \pm 5\}$.

For two data sets, each of size 5 , the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4 , respectively. The variance of the combined data set is