Question

The events $E_1,E_2,........$ represents the partition of the sample space $S$, if they are:

• A. pairwise disjoint
• B. exhaustive
• C. have non-zero probabilities
• D. All are correct

Answer 1

The correct option is D All are correct

A set of events $E_1,E_2,...$ is said to represent a partition of a sample space $S$, if

$\left(a\right)$ $E_i\cap E_j=\varphi ,i\ne j;i,j=1,2,3,...,n$ (pairwise disjoint)

$\left(b\right)$ $E_i\cup E_2\cup ...\cup E_n=S$ (exhaustive)

$\left(c\right)$ Each $E_i\ne \varphi ,i.e,P\left(E_i\right)>0$ for all $i=1,2,...,n$ (have non-zero probabilities)

That is the events should be pairwise disjoint, exhaustive and should have non zero probabilities.

Hence, option D is correct.