[Math] How to work out percentage/probability of recieving these marks

probabilitystatistics

I have a couple of maths question I want to ask, I am a computing student and I really want help with the answers to the following:

I am trying to state that if a test has more questions, then the relevance of getting questions answered correctly through guessing decreases. So if there is one question which has yes/no option to choose from, the chances of the student getting 100% in the exam is 50 per cent.

But what is the percentage if there are 50 questions each having yes/no options to gain the following full marks:

  • 100% (Full Marks)
  • 70% (Grade A)
  • 60% (Grade B)
  • 50% (Grade C)

If you can show formula on how this can be worked out then that would be great but if not it does not matter, the relevant thing is the correct percentags for each scenario.

Thanks

Best Answer

You can use binomial distribution that gives you the probability of $k$ successes out of $n$ trials when the success probability is $p$.

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In your case, $n=50$ and $k$ varies based on the percentage of correct answers. For example, $100\%$ means $k=50$, i.e. $50$ correct answers with probability $p=0.5$(since two choices yes or no are made with equal probability). Can you solve now for rest of the grades?

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