# Expected number of questions to win a game

1. Apr 3, 2013

### reg_concept

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.

2. Apr 3, 2013

### Staff: Mentor

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, ...)?

3. Apr 3, 2013

### reg_concept

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.
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.

4. Apr 3, 2013

### Staff: Mentor

Calculate the probabilities for that, and calculate the expectation value based on those probabilities?

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