Question

A pair of number cubes is rolled up.What is the probability that the sum is odd given that the sum is greater than or equal to 9.

• A. $\frac{1}{6}$
• B. $\frac{3}{28}$
• C. $\frac{2}{6}$
• D. $\frac{3}{5}$

Answer 1

The correct option is B $\frac{3}{28}$

A pair of cube is rolled.

Probability of getting sum equal to $9=\frac{4}{36}$

$=\frac{1}{9}$

$\Rightarrow$ As, total outcomes $=6^2=36$

Probability of getting a sum greater than $9$

i.e, $(4,6),(5,5),(5,6),(6,5),(6,6),(6,4)$

i.e, $\frac{6}{36}$

$=\frac{1}{6}.$

$\therefore$ Total probability $=\frac{1}{9}+\frac{1}{6}$

$=\frac{15}{54}$

$=\frac{3}{28}$

Hence, the answer is $\frac{3}{28}.$