Question

A pair of unbiased dice are rolled together till a sum of either 5 or 7 is obtained. Probability that 5 comes before 7 is

• A. $\frac{1}{5}$
• B. $\frac{2}{5}$
• C. $\frac{3}{5}$
• D. $\frac{4}{5}$

Answer 1

The correct option is B $\frac{2}{5}$

A-event that sum 5 occurs, B-sum 7 occurs
$P\left(A\right)=\frac{1}{9},P\left(B\right)=\frac{1}{6}$, probability that neither a sum 5 or 7 occur $P=\frac{13}{18}$
P=(Aoccurs before B)=$\frac{1}{9}+\left(\frac{13}{18}\right)\left(\frac{1}{9}\right)+....\infty =\frac{2}{5}$