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  • Please Solve R.D.Sharma class 12 Chapter 30 Probaility Exercise 30.5 Question 10 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 30 Probaility  Exercise 30.5 Question 10 Maths Textbook Solution.

Answers (1)

Answer:\frac{1}{3}

Hint: You must know the rules of finding probability and G.P series

Given: A and B toss a coin alternately till one of them get a heads and wins thegame

Solution: If A starts the game, then B will win only at even positions

P(winning the game) = P(head at 2nd turn + 4th turn + …….)

\begin{aligned} &\Rightarrow\left(\frac{1}{2} \times \frac{1}{2}\right)+\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)+\ldots \ldots \ldots . \\\\ &=\left(\frac{1}{2}\right)^{2}+\left(\frac{1}{2}\right)^{4}+\left(\frac{1}{2}\right)^{6}+\ldots \ldots . . \\\\ &\Rightarrow \frac{1}{4}\left[1+\left(\frac{1}{2}\right)^{2}+\left(\frac{1}{2}\right)^{4}+\ldots .\right] \\\\ &\Rightarrow \frac{1}{4}\left[\frac{1}{1-\frac{1}{4}}\right] \quad\left[\text { For G.P: } 1+a+a^{2}+a^{3}+\ldots=\frac{1}{1-a}\right] \\\\ &\Rightarrow \frac{1}{4} \times \frac{4}{3} \\\\ &\Rightarrow \frac{1}{3} \end{aligned}

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