Question

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

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

Answer 1

The correct option is C $\frac{11}{36}$

$P$(rolling a seven) $=P\left(A\right)=\frac{6}{36}=\frac{1}{6}$
$P$( not rolling a seven) $=P\left(B\right)=1-P\left(A\right)=\frac{1-1}{6}=\frac{5}{6}$
Here, we may observe that it is certain we will either roll a $7$ at least once or not roll a seven
$P\left(C\right)+P\left(B\right).P\left(B\right)=1P\left(C\right)=1-{\left(P\left(B\right)\right)}^2$
$P\left(C\right)=1-{\left(\frac{5}{6}\right)}^2=1-\frac{25}{36}=\frac{11}{36}$