Question

Match $\text{List I}$ with the $\text{List II}$ and select the correct answer using the code given below the lists :
A pair of dice is rolled and the sum of the numbers that comes up is noted down, then consider the following events
$A=$ sum of numbers is odd
$B=$ sum of numbers is even
$C=$ sum of numbers is more than $11$
$D=$ sum of numbers is less than $4$
$E=$ sum of numbers is prime number

$\begin{array}{cccc}& \text{List-I}& & \text{List-II}\\ \text{(a)}& A\text{and}B& \text{(p)}& \text{Simple event}\\ \text{(b)}& C\text{and}D& \text{(q)}& \text{Exhaustive events}\\ \text{(c)}& B\cap C& \text{(r)}& \text{Exclusive events}\\ \text{(d)}& A\text{and}E& \text{(s)}& \text{Equally likely event}\end{array}$

Which of the following is correct combination?

• A. $\text{(a)}\to \text{(q)},\text{(b)}\to \text{(r)},\text{(c)}\to \text{(p)},\text{(d)}\to \text{(s)}$
• B. $\text{(a)}\to \text{(r)},\text{(b)}\to \text{(q)},\text{(c)}\to \text{(p)},\text{(d)}\to \text{(s)}$
• C. $\text{(a)}\to \text{(p)},\text{(b)}\to \text{(q)},\text{(c)}\to \text{(s)},\text{(d)}\to \text{(r)}$
• D. $\text{(a)}\to \text{(s)},\text{(b)}\to \text{(q)},\text{(c)}\to \text{(r)},\text{(d)}\to \text{(p)}$

Answer 1

The correct option is A $\text{(a)}\to \text{(q)},\text{(b)}\to \text{(r)},\text{(c)}\to \text{(p)},\text{(d)}\to \text{(s)}$

The sample space $S=\{2,3,4,5,6,7,8,9,10,11,12\}$
$A=$ Sum of nos. is odd
$=\{3,5,7,9,11\}$
$B=$ Sum of nos. is even
$=\{2,4,6,8,10,12\}$
$C=$ Sum of nos. is more than $11$
$=\left\{12\right\}$
$D=$ Sum of nos is less than $4$
$=\{2,3\}$
$E=$ Sum of nos. is prime no.
$=\{2,3,5,7,11\}$

$A\cup B$ will contain all the elements $A\cup B=\{2,3,4,5,6,7,8,9,10,11,12\}$
So, $A$ and $B$ is exhaustive events.

$C\text{and}D$ does not have any common element, so they are exclusive events.

$B\cap C=\left\{12\right\}$ has only one element, so it is a simple event.

$A\text{and}E=$ both have equal no. of elements, so they are equally likely events.