Two persons A and B throw three unbiased dice one after the another. If A gets the sum 13 , then the…
Two persons A and B throw three unbiased dice one after the another. If A gets the sum 13 , then the probability that $B$ gets higher sum is
$\frac{5}{216}$
$\frac{4}{27}$
$\frac{35}{216}$
$\frac{20}{216}$
Solution
Total possible outcomes when 3 dice are thrown are $6^3=216$
Outcomes of type $(6,6, \ldots)=3 \times 4=12$
Outcomes of type $(6,5, \ldots)=3+2 \times 3!=15$
Outcomes of type $(6,4, \ldots)=3$
Outcomes of type $(5,5, \ldots)=3+1=4$
and $(6,6,6)$
Probability $=\frac{12+15+4+3+1}{216}=\frac{35}{216}$.