What is the probability that you knew the answer to a question, given that you answered it correctly?

Question

Suppose you are taking a multiple-choice test with 4 choices for each question. In answering a question on this test, the probability that you know the answer is 0.7. If you don't know the answer, you choose one at random.

Answer 1

IF you don't know the answer and choose at random, your probability of getting it right is 1/4 = 25%

IF you have some information about the problem, you apprently will get it right 70% of the time. 0.70 = 70%

Pure guess gets 25% right. Educated "guess" gets it 70% right.

Or maybe what this problem really meant was guessing gets 25% right and you get it right 100% if you know the answer, and you will get a 70 grade on this test, so how many did you guess, and how many did you know?

25X + 100Y = 70(X+Y)

if you got an equal number guessing as the number you knew the answer to, then your grade would have been (25+100)/2 = 125/2 = 62.5 But you got 70, meaning you knew more questions than you guessed on, but just slightly more, to get a 70.

Let's say there were 100 questions, multiple choice with 4 choices per each question

then 25X +100(100-X) = 70(100) = 7000

25X [phone]X = 7000

75 X = 3000

X = 3000/75 = 1000/25 = 40 guesses, 60 you got right because you knew the answer

You guessed on 40% of the questions, and you knew 60% of the answers

40% of 100 was 40 questions and you got 1/4 right or 10. you knew 60% of 60 getting 60 right

grand total was 10+60 right or 70%