NIMCET 2009 — Mathematics PYQ
NIMCET | Mathematics | 2009and throw a die in succession to win a bet with starting first. Whoever throws '1' first wins an amount of Rs. 110. What are the respective expectations of and ?
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and throw a die in succession to win a bet with starting first. Whoever throws '1' first wins an amount of Rs. 110. What are the respective expectations of and ?
1. Determine Individual Probabilities
For a single throw of a fair die:
Probability of throwing '1' (Success), .
Probability of not throwing '1' (Failure), .
2. Probability of A Winning ()
wins if they throw '1' on the 1st, 3rd, 5th, ... throw.
1st throw:
3rd throw: (A fails, B fails, A succeeds)
5th throw:
This forms an infinite geometric progression:
3. Probability of B Winning ()
Since one of them must eventually win:
4. Calculate Expectations
Expectation is defined as .
Expectation of A:
Expectation of B:
Conclusion:
The respective expectations for and are Rs. 60 and Rs. 50.
Final Answer:
The correct option is (b) Rs. 60 and Rs. 50.