Question

A pair of dice is thrown at a time . $X$ is the maximum of two numbers shown on the dice. The mean of $X$ is

• A. $\frac{151}{36}$
• B. $\frac{161}{36}$
• C. $\frac{141}{36}$
• D. $\frac{131}{36}$

Answer 1

The correct option is B $\frac{161}{36}$

$\to$ Cases when $x=6$;

$(6,1)...\left(\right)6,6,(1,6)...(5,6)=11$

with $x=5;9$

$x=4;7$

$x=3;5$

$x=2:3x=1:1$

$\Rightarrow$ Mean $=\frac{66+45+28+15+6+1}{11+9+7+5+3+1}$

$=\frac{161}{36}\Rightarrow \left(B\right)$