Question

Consider events A, B, C, D, E of the sample space S$=\{$:n is an integer such that $10\le n\le 20\}$ given by.
A is the set of all even numbers.
B is the set of all prime numbers.
C$=\left[15\right]$.
D is the set of all integers $\le 16$.
E is the set of all double digit numbers expressible as a power of $2$.

A, and B are.

• A. Mutually exclusive events but not exhaustive events
• B. Exhaustive events but not mutually exclusive events
• C. Mutually exclusive and exhaustive events
• D. Elementary events

Answer 1

Answer: (A)

Mutually exclusive events but not exhaustive events

Expressing all sets as mathematical expressions

$A=[10,12,14,16,18,20]$

$B=[11,13,17,19]$

$C=\left[15\right]$

$D=[10,11,12,13,14,15,16]$

$E=\left[16\right]$

now considering sets $A$ and $B$ both have no element is common they are mutually exclusive sets but they are not exhaustive too because they cant't be happen simultaneously and they didn't maintain all elements in union.