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

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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