Explanation
1. Determine Individual Probabilities
For a single throw of a fair die:
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Probability of throwing '1' (Success), p=61.
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Probability of not throwing '1' (Failure), q=1−61=65.
2. Probability of A Winning (P(A))
A wins if they throw '1' on the 1st, 3rd, 5th, ... throw.
This forms an infinite geometric progression:
P(A)=1−q2p=1−(5/6)21/6=1−25/361/6
P(A)=11/361/6=61×1136=116
3. Probability of B Winning (P(B))
Since one of them must eventually win:
4. Calculate Expectations
Expectation is defined as P(winning)×Amount.
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Expectation of A:
Exp(A)=P(A)×110=116×110=6×10=Rs. 60
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Expectation of B:
Exp(B)=P(B)×110=115×110=5×10=Rs. 50
Conclusion:
The respective expectations for A and B are Rs. 60 and Rs. 50.
Final Answer:
The correct option is (b) Rs. 60 and Rs. 50.