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  • A coin is tossed repeatedly. A and B call alternately for winning a prize of Rs 30 . One who calls correctly first wins the prize. A starts the call. Then the expectation of.<div class='qna-opt

A coin is tossed repeatedly. A and B call alternately for winning a prize of Rs 30 . One who calls correctly first wins the prize. A starts the call. Then the expectation of.

Option: 1

A is Rs 10


Option: 2

B is Rs 10


Option: 3

A is Rs 20


Option: 4

B is Rs 20


Answers (1)

best_answer

The probability of A winning

\mathrm{=P(A)+P(\bar{A} \bar{B} A)+P(\bar{A} \bar{B} \bar{A} \bar{B} A)+\ldots }
\mathrm{=\frac{1}{2}+\left(1-\frac{1}{2}\right)\left(1-\frac{1}{2}\right) \frac{1}{2}+\ldots=\frac{1}{2}+\left(\frac{1}{2}\right)^3+\ldots=\frac{\frac{1}{2}}{1-\frac{1}{4}}=\frac{2}{3} }

\mathrm{\therefore \quad} the probability of B winning \mathrm{=1-\frac{2}{3}=\frac{1}{3}}
\mathrm{\therefore \quad} the expectation of A \mathrm{=\operatorname{Rs} 30 \times \frac{2}{3}=\operatorname{Rs} 20}, and

the expectation of B \mathrm{=\operatorname{Rs} 30 \times \frac{1}{3}=\operatorname{Rs} 10}.

Posted by

Devendra Khairwa

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