Question

Two dice are thrown simultaneously, what is the probability of not getting the sum of the digits on the dice as '2'?

• A. $\frac{11}{36}$
• B. $\frac{35}{36}$
• C. $\frac{1}{6}$
• D. $\frac{2}{3}$

Answer 1

The correct option is B $\frac{35}{36}$

Total number of outcomes = 36
Outcome where the sum of digits is '2' is {(1, 1)}.
$\therefore$Total number of favourable outcomes =1

For an event $\text{E,}$
$\text{Probability P(E)}=\frac{\text{Number of outcomes favorable to E}}{\text{Number of all possible outcomes of the experiment}}$

$\therefore$ P(Sum of digits is '2' ) = $\frac{1}{36}$

Since, for an event $\text{P(E)}+P\left(E^{\prime }\right)=1$
$\therefore$P(Sum of digits not '2' )
$=1-\frac{1}{36}=\frac{35}{36}$