Expected number of questions to win a game

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Discussion Overview

The discussion revolves around calculating the expected number of questions a participant needs to answer in a quiz competition to win, given specific rules about scoring and penalties for incorrect answers. The focus is on the probabilistic aspects of the game and the implications of guessing answers randomly.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant describes the rules of the quiz competition, noting that a player wins by scoring 5 points but faces a reset of points after two consecutive wrong answers.
  • Another participant questions whether the player is guessing randomly and suggests that the expected number of questions depends on the player's knowledge.
  • It is clarified that the player is assumed to guess randomly, with a probability of 1/3 for each question being answered correctly.
  • A participant expresses difficulty in calculating the expected value for winning when the target score is 1, suggesting that the expected value could be derived from the probabilities of different outcomes.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the expected number of questions needed to win, and multiple viewpoints regarding the assumptions about guessing and knowledge remain present.

Contextual Notes

There are unresolved mathematical steps related to calculating the expected value based on the probabilities of answering questions correctly and the implications of scoring resets.

reg_concept
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Let, a person is taking part in a quiz competition.
For each questions in the quiz, there are 3 answers, and for each correct answer he gets 1 point.
When he gets 5 points, he wins the game.
But, if he gives 2 consecutive wrong answers, then his points resets to zero (i.e. if his score is now 4 and he gives 2 wrong answers, then his score resets to 0).

My question is, on an average how much questions he needs to answer to win the game?
Plz, someone give answer.
 
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It depends on his knowledge ;).
Are you assuming he guesses randomly?

If this is homework, what did you try so far? Did you consider easier examples (1, 2, 3 points to win, ...)?
 
mfb said:
Are you assuming he guesses randomly?
Yes that's why it is a problem of probability :) His chance of picking the right answer is 1/3, since there are 3 questions per questions.
mfb said:
If this is homework, what did you try so far? Did you consider easier examples (1, 2, 3 points to win, ...)?
No, it is not a homework problem.

I tried but could not solve. If the point to win is 1, then he can make it at the first chance, or after 2 chances, or after 3 chances, so on... .But what should be the expected value?
I can't solve.
 
reg_concept said:
If the point to win is 1, then he can make it at the first chance, or after 2 chances, or after 3 chances, so on... .But what should be the expected value?
Calculate the probabilities for that, and calculate the expectation value based on those probabilities?
 

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