QJEEM25Macc4c: JEE Main 2025 Mathematics - Class 12 JEEM25Macc4c Solution: and alternately throw a pair of dice. A wins if he throws a sum …

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QJEEM25Macc4c: JEE Main 2025 Mathematics - Class 12 JEEM25Macc4c Solution: and alternately throw a pair of dice. A wins if he throws a sum …

$A$ and $B$ alternately throw a pair of dice. A wins if he throws a sum of 5 before $B$ throws a sum of 8 , and $B$ wins if he throws a sum of 8 before $A$ throws a sum of 5 . The probability, that A wins if A makes the first throw, is

Multiple Choice Options

A $\frac{8}{19}$
B $\frac{9}{19}$
C $\frac{8}{17}$
D $\frac{9}{17}$

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Accepted Answer

$\begin{aligned} p (S_{5}) = \frac{1}{9} \\ p (S_{5}) = \frac{5}{36} \\ required prob = \frac{1}{9} + \frac{8}{9} \cdot \frac{31}{36} \cdot \frac{1}{9} + {(\frac{8}{9} \cdot \frac{31}{36})}^{2} \cdot \frac{1}{9} + \dots \infty \\ = \frac{\frac{1}{9}}{1 - \frac{62}{81}} = \frac{9}{19} \end{aligned}$

QJEEM25Macc4c: JEE Main 2025 Mathematics - Class 12 JEEM25Macc4c Solution: and alternately throw a pair of dice. A wins if he throws a sum …

Multiple Choice Options

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