Question

The chance of throwing at least $9$in a single throw with two dice is

• A. $\frac{1}{18}$
• B. $\frac{5}{18}$
• C. $\frac{7}{18}$
• D. $\frac{11}{18}$

Answer 1

The correct option is B

$\frac{5}{18}$

Explanation for the correct option

Finding the probability

Sample space for sum to be not less than $9$ =$\left\{\right(6,4),(4,6),(6,5),(5,6),(5,5),(6,6),(3,6),(3,6),(5,4),(4,5\left)\right\}$

$9$ can be made up in $4$ ways, and thus the chance of throwing $9$ $=\frac{4}{36}$($4$ ways of getting sum as $9$)
$10$ can be made up in $3$ ways, and thus the chance of throwing $10$ $=\frac{3}{36}$($3$ ways of getting sum as $10$)
$11$ can be made up in $2$ ways, and thus the chance of throwing $11$ $=\frac{2}{36}$($2$ ways of getting sum as $11$)

$12$ can be made up in $1$ way, and thus the chance of throwing $12$ $=\frac{1}{36}$($1$ way of getting sum as $12$)
Now the chance of throwing a number not less than $9$ is the sum of these chances separately.
Therefore, the required chance is,

$=\frac{4+3+2+1}{36}$

$=\frac{5}{18}$

Hence, the correct answer is Option (B).