Question

Two fair dice are thrown. What is the probability that the two scores do not add to $5$?

• A. $\frac{7}{9}$
• B. $\frac{5}{9}$
• C. $\frac{8}{9}$
• D. $\frac{1}{9}$

Answer 1

The correct option is C $\frac{8}{9}$

There are $36$ possible ways two dice can land, and of these $4$ of them add to $5$ i.e.
$1+4=5$
$2+3=5$
$3+2=5$
$4+1=5$
$P$ (The two scores do add to $5$) $=$ $\frac{4}{36}=\frac{1}{9}$

$P$ (The two scores do not add to $5$) $=$ $1-\frac{1}{9}=\frac{8}{9}$