Question

A die is numbered in such a way that its faces show the numbers $1,2,2,3,3,6$. It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two throws:
What is the probability that the total score is
(i) even? (ii) $6$? (iii) at least $6$?

Answer 1

$+$	$1$	$2$	$2$	$3$	$3$	$6$
$1$	$2$	$3$	$3$	$4$	$4$	$7$
$2$	$3$	$4$	$4$	$5$	$5$	$8$
$2$	$3$	$4$	$4$	$5$	$5$	$8$
$3$	$4$	$5$	$5$	$6$	$6$	$9$
$3$	$4$	$5$	$5$	$6$	$6$	$9$
$6$	$7$	$8$	$8$	$9$	$9$	$12$

Total no. of possible outcomes when 2 dice are thrown $6\times 6=36$

i) Total times when the sum is even $=18$

$P\left(\text{Getting an even no.}\right)=\frac{18}{36}=\frac{1}{2}$

ii) Total times when the sum is 6 $=4$

$P\left(\text{Getting sum as 6}\right)=\frac{4}{36}=\frac{1}{9}$

iii) Total times when the sum is atleast 6 $=15$

$P\left(\text{Getting sum atleast 6.}\right)=\frac{15}{36}=\frac{5}{12}$