Question

Calulate the probability of scoring a total of $7$ once in two tosses of a pair of fair dice.

• A. $\frac{1}{36}$
• B. $\frac{5}{18}$
• C. $\frac{1}{3}$
• D. $\frac{11}{36}$

Answer 1

The correct option is B $\frac{5}{18}$

$P$(rolling a seven) $=P\left(A\right)=\frac{6}{36}=\frac{1}{6}$
$P$( not rolling a seven) $=P\left(B\right)=1-P\left(A\right)=\frac{1-1}{6}=\frac{5}{6}$
So required probability of rolling a seven and not a seven or not rolling a seven and rolling a seven
$P\left(C\right)=P\left(A\right).P\left(B\right)+P\left(B\right).P\left(A\right)=2P\left(A\right)P\left(B\right)=2\times \frac{1}{6}\times \frac{5}{6}=\frac{5}{18}$