Expected number of questions to win a game

[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.

 

[mfb]

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, ...)?

 

[reg_concept]

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.

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.

 

[mfb]

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?

 

[blue_raver22]

I would approach this question by first defining the variables involved. In this case, we have the number of points needed to win the game (5), the number of answers per question (3), and the possibility of a score reset after 2 consecutive wrong answers.

Next, we can use probability to determine the expected number of questions needed to win the game. For each question, there is a 1/3 chance of getting the correct answer and a 2/3 chance of getting it wrong. Therefore, the probability of getting 5 consecutive correct answers and winning the game is (1/3)^5 = 1/243.

However, since there is also the possibility of a score reset after 2 consecutive wrong answers, we need to consider the probability of getting 2 wrong answers in a row. This probability is (2/3)^2 = 4/9.

Therefore, the overall probability of winning the game is (1/243) * (5/9) = 5/2187.

To find the expected number of questions needed to win the game, we can use the formula:
Expected number of questions = 1/probability

Therefore, the expected number of questions needed to win the game is 2187/5, which is approximately 437.4.

However, it is important to note that this is an average and the actual number of questions needed to win the game may vary. It is also possible for the game to go on for much longer than the expected number of questions.

In conclusion, the expected number of questions needed to win the game is approximately 437.4, but this can vary depending on the individual's performance and luck.