Monday, 12 December 2011


ok let's play probability game
in a test, the passing mark is 50.
there are 50 true or false answer. each correct Q will add 1 mark but each wrong ans will deduct 0.5 mark
then there are 10 essay Qs that have 5 mark each......

assuming that the student only scores 20 to 30 marks for his essay Q, what is the probability of the student to pass?


  1. Okay, before I try to answer your question, I just want to point out that it is quite subjective because we don't get to analyse all the possible factors that could contribute to the probability for the student to pass especially in terms of the student's academical abilities. He/she may not be excellent in writings for instance, but may perform really well in terms of factual knowledge.

    The question is also ambiguous in terms of the nature of the test the student is taking. It could be a personality test, which would again be a little biased for the student if he/she may not be good in expressing him/herself in the essay writings. Also, what kinda test has 10 essay questions? Hahahah! But anyway, here goes...

    Assuming that the student managed to score 20 - 30 marks for his essay questions, he would need to score another 20 - 30 marks for the true or false questions.

    So let's say that he has scored 25 marks for his essay questions, he would have to score another 25 marks for the true or false questions.

    This means, he has to answer 33 questions correctly in order to gain a total of 24.5 marks, which would be rounded off to 25 marks if it is marked according to the Malaysian examination marking scheme. But to be safe, let's say that he needs to answer 34 questions correctly and score 26 marks so we could put him just above the passing mark.

    Now, to work out the probability, assuming that his intelligence for essay writings is equal to his intelligence of factual knowledge tested in the form of true or false questions:

    P (Essay) = 25/50 = 1/2

    Based on the probability, the student would only score half of the total of true or false questions correctly giving a total of 12.5/13 marks, derived from a total of 25 marks for every 25 questions answered correctly and a deduction of 12.5 marks for every 25 questions answered incorrectly.

    Given the circumstances, he/she is predicted to score a total of 37.5/38 marks out of 100 marks. But to pass the test, he/she needs just another 12.5/13 marks. So, the probability for he/she to pass the test is:

    P (Test) = 37.5/50 = 3/4


    P (Test) = 38/50 = 19/25

    Hence, again, assuming that his intelligence for both essay writings and true or false questions is equal, it would be approximately 3 out of 4 outcomes that the student will pass the test. Am I right?

    Phew... Your game bikin penat. Haha! But it's fun. :)

  2. ni macam style MTF kat india je..

  3. huhu i want to reply to your comment but as you know i was having an exam at that time so i cant.
    actually there's no calculation needed to answer this Q. the reason is because, the 50 questions of true or false only provide 2 choices of answer so the probability to get the answer right is 50%. 50% for wrong answer too. so, it doesnt matter how many marks one try to get, the probability to get the mark is still 50%. in other words, the chance for one to get full mark(jackpot) is 50% and so does for 0.
    in order to get pass, the student will have to rely on the essays questions to get marks as high as the student can and get luck on his side. that is by studying. that will eventually increase the percentage of getting right on the true or false question.

    anyway, thank you for trying to solve my silly game

    p/s: i forgot it was short essay question and this was made based on my exam ^^

    wak: bukan macam tp mmg sama pon

  4. Hahah! You know what... I did thought about the 50-50 answers too. But something tells me that it just doesn't glue. I still don't know what is not gluing, to be honest... So I took a more complicated analysis to solve your game. But yes, I can see that you did it the other way round - relying on the essay questions. Which, is not wrong, but is just too subjective for me. And I can't stand it! Hence, my version of the solution for the game. :B

    Oh, no problem really. I enjoyed it! My maths was a bit rusty though.

    Ohh... Patutla. Hairan juga napa ada 10 essay questions. I was horrified. :D

  5. haha nobody would have 10 long essays for exam. that is creaaazy.. haha yeah i know how you feel, subjective answer for math just dont fit in.... but i still can understand the last part where you get 3/4. did you use calculator?