Explain Solution R.D. Sharma Class 12 Chapter 30 Probability  Exercise 30.5 Question 37 Maths Textbook Solution.

Answers (1)

Answer:

P\left ( A\: wins \right )=\frac{6}{11}

P\left ( B\: wins \right )=\frac{5}{11}

Hint: You must know the rules of finding probability functions.

cgfyTill one of them gets the sum of numbers as multiples of 6 and wins the game.

Solution: Let S denote the success and F denote the failure (not getting 6)

Thus,

\begin{aligned} &P(\mathrm{~S})=\frac{1}{6}=\mathrm{p} \quad, \quad P(\mathrm{~F})=\frac{5}{6}=q \\\\ &P(\mathrm{~A} \text { wins the first throw })=P(\mathrm{~S})=p \\\\ &P(\mathrm{~A} \text { wins the third throw })=P(\mathrm{FFS})=q q p \\\\ &P(\mathrm{~A} \text { wins the fifth throw })=P(\mathrm{FFFFS})=q q q q p \end{aligned}

So,

\begin{aligned} &P(\mathrm{~A} \text { wins })=p+q q p+q q q q p+\ldots \\\\ &=p\left(1+q^{2}+q^{4}+\ldots\right) \\\\ &=\frac{p}{1-q^{2}}=\frac{\frac{1}{6}}{1-\frac{25}{36}}=\frac{6}{11} \\\\ &P(\mathrm{~B} \text { wins })=1-\frac{6}{11}=\frac{5}{11} \\\\ &\therefore P(\mathrm{~A} \text { wins })=\frac{6}{11} \quad, \quad P(\mathrm{~B} \text { wins })=\frac{5}{11} \end{aligned}

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