Probability you should know before college

This is a nice conditional probability question adapted from an admissions test. #math #maths #mathematics #shorts

IUT 2016-17 Admission Test MCQ 85

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[kimitsudesu]

Not to critique your creative process, but making this problem into a test question with 4 answers would be neat...

[toaster]

Out of 300 questions, he knows 200, and on the remaining 100 he guesses 25 of them correctly. So 25/225 correct answers were by guessing. 25/225 = 1/9.

[aguyontheinternet]

I tried to solve it in the way you described, but I got stuck, and so I ran a simulation of 144 students on my paper. Out of the 144, 96 knew the answer, while 48 did not, but 12 students got the answer anyways. This was a total of 108 students that got the answer right, and 12 of them guessed. This gave me a probability of 1/9, when you simplify.

[hareecionelson]

this is how screening results for common diseases are interpreted, and why screening is only useful when the base rate of disease is high

[Uejji]

Take 12 students. 2/3 (8) of them mark the correct answer due to knowing the answer. The remining 4 are guessing. Let each guessing student pick 1 of the 4 answers. Thus, 9 students picked the correct answer, with 1 of those 9 guessing. Thus 1/9

[benkaplun]

Anyone else solve this with Bayes Theorem?

[TheFoxMaster]

I thought the question asked if the previous question was marked correctly what was the chance of him being on a question which he was guessing not guessing a correct answer I'm not sure if that's me not understanding the question or it being badly worded

[samarpratap]

Wow, a question in a question
Inception of question

[sparshsharma]

Classic representation of iconic Bayes Theorem!

[mrunankBathe]

God help him if it is negative marking

[MarsJenkar]

I visualized this with three sets of four multiple-choice bubbles. The first two, where the student knew the answer, had all the bubbles filled in, representing a known correct answer. The third, where the student was randomly guessing, had only the one bubble filled in. I then surmised that the answer was one out of nine, with the one corresponding to the lone bubble in the third row, and the nine corresponding to all the filled bubbles.

Honestly, I'm amazed that trick worked here, but there it is.

[animezoneamv]

Not gonna lie. As a 11th grade student who learned calculus already, I couldn't even understand this question properly.

[kanikgupta]

Simple, 1/9 using Bayes' Theorem(Probability)

[lukeheatley]

make sense.

if 8 out of 12 answers are known/correct and 1 out of 12 is guessed/correct, then of the total 9 correct, just one is guessed.

so the answer is a ninth.

[boas_]

Me not knowing that marking an answer means picking that answer lol

[antrikshsingh]

I mean its a proper standard question of the Baye's theorem, takes like 5 seconds to solve with it...

[Absurdated]

Prior log odds of ignorance: log(1:2) ≈ -3 dB
Evidence: log(1/4:1) ≈ -6 dB
Posterior odds: -3 + -6 = -9 dB, odds 1:8, p=1/9.

[Trizzer]

You don't need to draw anything. 8/12 not guessing. 1/12 guessing. Thus 1/9

[mustafaissa]

But he can know and get it wrong, like solving the question wrong so he thinks that he know it

[レン-up]

Is this another one of those confidence boosters or what? 😩