Question

A player throws 2 ordinary die with faces numbered 1 to 6. What is the probability of obtaining a total score of atmost $6$?

• A. $12/36$
• B. $16/36$
• C. $15/36$
• D. $10/36$

Answer 1

The correct option is C $15/36$

Total number of elements in the sample set
$=6^2$
$=36$.
Now favorable elements include
$(1,1)\to (1,5)$ 5 elements.
$(2,1)\to (2,4)$ 4 elements.
$(3,1)\to (3,3)$ 3 elements.
$(4,1)\to (4,2)$ 2 elements.
$(5,1)\to (5,1)$ 1 element.
Hence total number of favorable elements
$=5+4+3+2+1$
$=15$.
Hence the required probability
$=\frac{15}{36}$