# 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?

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?