Probability of failing 80% in an exam

[minitine]

Question:

A student is given an option to take the final test or get a grade of 75%. If he takes the test and passes, he will be given a grade of at least 84, a minimum rating he needs for his scholarship. If he takes the test and fails, he will definitely be given a final grade of 70. The probability of his failing the test is 80%. Should the student take the test or not?

ANSWER: Yes, because he still have at least 20% to pass the exam, given that he would make the rightful decisions in studying and preparing for the exam.

Is this a good answer or not?

 

[Romsek]

One can look at the expected value for their final grade

If they don't take the test their final grade is 75%

If they take it the expected value for their final grade is

[MATH]\dfrac 1 5 \cdot 84 + \dfrac 4 5 \cdot 70 = \dfrac{364}{5} = 72.8 < 75[/MATH]
On this basis they should not take the test.

However if an 84 is needed to get the scholarship then really the student has no choice.
They must try to pass the exam.

 

[Steven G]

The student has two choices--take the test or not take the test.

If he does not take the test he gets a 70% on the test and loses his scholarship. This option is not good at all.

If he takes the test he has a chance of passing the test (>0%)and get at least 84% and continue to receive his scholarship. This option gives the student some hope.

It is obvious that he should take the test!

 

[Steven G]

Question:

A student is given an option to take the final test or get a grade of 75%. If he takes the test and passes, he will be given a grade of at least 84, a minimum rating he needs for his scholarship. If he takes the test and fails, he will definitely be given a final grade of 70. The probability of his failing the test is 80%. Should the student take the test or not?

ANSWER: Yes, because he still have at least 20% to pass the exam, given that he would make the rightful decisions in studying and preparing for the exam.

Is this a good answer or not?

No, I do not think it is a good answer and here is why. Studying or not he has a 20% chance of passing the test and if he passes he keeps his scholarship. You stated this, very good. However you never mention that if he chooses not to take the test what would happen. You should have said that if he doesn't take the test he will certainly lose his scholarship. In the end, as slim as his chances of passing the test are, he has a chance of keeping his scholarship if he takes the test and no chance of keeping his scholarship if he dos not take the test.

It could have been that if he does not take the test then he will be given a 85% on the test and hence keep his scholarship. In that case he should not take the test. In this case it would still be true that if he takes the test he will have a 20% chance of passing it as you said in your answer but now the right choice is completely reversed and your response is not valid anymore. Do you see what I am saying??