Probability theory

[abstibus]

Any mathematics gurus out there?
An examination question is in paragraphs with 25 spaces. Each space has one correct and one incorrect answer.
What is the probability of candidates achieving 100% overall?

[THECORBYLOON]

If there are 25 spaces each with 2 outcomes, the probability is 1 in 2^25 or 1 in 33554432

[THECORBYLOON]

This is if each answer is picked at random

[Gizmonster]

Maybe I'm misunderstanding things here - but the way I interpret it, there are 25 spaces/questions and there's a 50% chance of getting each one correct ...... therefore the chance of getting them all correct are 2^25 = 1 in 33554432 chance.
Am I missing something ???

[THECORBYLOON]

Is that not what I said?

[THECORBYLOON]

Oddly enough, when I was typing the answer I had used 1/(2^25) but decided it looked awkward and changed it

[factor-fiction]

You could type it as 1 in 2²⁵ but that's difficult to read.
As someone said, this assumes answers are chosen at random. In practice you would expect the student to be able to know the answer to some questions or make an educated guess

[abstibus]

Thanks, all
You've given me the evidence to confront the 'doubter', who insisted that students would either know the answer or make an educated guess and get 100%
I disagreed, but had no way to start countering his argument.
Hah!

[venator]

In many schools these days, the teacher would have coached the class, so there's a higher probability.

[abstibus]

What does this ^ stand for?
TIA

[abstibus]

I see - it's 'to the power of'.

[venator]

Hang on chaps, read the question - OP doesn't say that the answers are chosen at random!

She does say that they are being chosen by candidates, who presumably know something of the subject. - see my earlier post.

The probility is therefore - in the real world -much lower, but cannot be calculated from the given data.

[factor-fiction]

Hang on venator, read the answers. This point has already been covered.

[abstibus]

Venator
I know that probability is lower, but the doubter is such a know-all that I had to do something.
Say candidates knew the definitive answer to 10 questions and tried to make a guess at 15 questions (just surmising), what would then be the probability? Would it be 1 ^ 15?
(I have no idea how to work this out)

[THECORBYLOON]

I know the OP didn't say it was random which is why I added the second answer. It's like the probability of a coin landing on heads which, for practical purposes, is 0.5 or 50/50. Strictly, it's less than 0.5 but assumptions have to be made.

[ChuckFickens]

1^15 is 1

It would be 2^15 as they would only be guessing 15 question so the others can be ignored in your example.

In reality they would probably be making educated guesses rather than random guesses.

[ChuckFickens]

Sorry, should have said, the probability would be 1/32768

[abstibus]

Armed with this, I will venture into the fray, with banners and pennants flying!!!
He reckons he knows everything - but he doesn't know about AB.

[THECORBYLOON]

Even if a candidate knew twenty-four answers and had to guess the other, there's a 50/50 chance of getting it wrong so it must be less than 100% but if it were 100%, what would be the point of the test?