Question

Two dice are thrown. What is the probability of scoring either a double, or a sum greater than $9$ ?

• A. $\frac{1}{3}$
• B. $\frac{1}{9}$
• C. $\frac{5}{18}$
• D. $\frac{1}{18}$

Answer 1

Answer: (C)

$\frac{5}{18}$

Total number of cases$=36$
Let $A=$$A=\{(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)\}$
$B=\{(4,6),(5,5),(6,4),(5,6),(6,5),(6,6)\}$
$\therefore A\cap B=\{(5,5),(6,6)\}$
Now, $P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$=\frac{6}{36}+\frac{6}{36}-\frac{2}{36}=\frac{10}{36}$
$\Rightarrow P(A\cup B)=\frac{5}{18}$