Thread: Probability question

Hello, new to these forums. I have a question - apologies if it is fairly simple to work out the answer, but my mathematical ability is limited.

Story here: BBC NEWS | Asia-Pacific | Woman passes 950th driving test

A Korean woman passed her driving theory test on the 950th go. The test consists of 50 multiple choice questions with 4 possible answers. You need to get more than 60% to pass the test. I was wondering what were the chances of passing the test simply randomly. I think that if you're purely guessing the chances are you should get around 25% right, and that the chance of getting 100% in the test is 1 in 4^50 (correct me if I'm wrong), but I can't figure out a simple method to generate results in between. I've been working on this for hours now but given my lack of knowledge I'm finding it hard to solve!

Edit: on checking that story I've noticed that it doesn't say each multiple choice question has 4 answers, not sure where I got that from, but could someone please answer with that assumption anyway.

I think I'm going to have to disappoint you. You're highly unlikely to solve it by chance.

You can do this with Binomial distribution. So if you plug the values in to this link: Binomial Distribution: Probability Calculator
0.25 - Chance of getting a question right
50 - Number of trial/questions
30 - Number of successes (questions you need to answer correctly to pass)

You want the P(X >= 30) value. Which is 1.64228554977441E-07. If you plug this in again:
1.64228554977441E-07
950
1

The chance of her passing 1 or more times by chance in those 950 is approximately 0.000156 or 1 in 6410.

Thanks very much for that - it's certainly a lot more unlikely than I would have intuitively guessed!