Illuminati-R-Us

I just took an online quiz with 10 football questions on an expert level. Each question had 4 possible answers. I got 1 (one) question out of ten right.

That was somewhat depressing - not because I fancy myself a football expert, the questions really were much too hard for my level of knowledge. But I think I did a good deal worse than I would have usually done by chance alone.

Can anyone here calculate what the p-value is for getting one out of ten right if the null hypothesis is that this quiz is ruled by chance alone?

Just out of interest, if anyone feels up to it AND sufficiently interested.

I bet you did better than I would have.

Maybe, but you'd have a fair shot at getting two or three right just by answering villy-nilly.

If there is a 1/4 chance of getting each question right, and those are independent events, the probabilities of the eleven possible scores are as shown below.

0 0.056313514709473
1 0.187711715698242
2 0.281567573547363
3 0.250282287597656
4 0.145998001098633
5 0.058399200439453
6 0.01622200012207
7 0.003089904785156
8 0.000386238098145
9 2.86102294921875E-05
10 9.5367431640625E-07

So the probability of getting 0 or 1 questions correct when throwing darts is 0.244025230407715.

Many thanks, so I was comfortably inside what chance alone could have plausible given me - I had a 1 in 4 chance of getting one or less by chance alone.

Linky?

Мастер wrote:Linky?

What he said.

But you had a higher probability of getting a total of 2 correct answers, so sit the exam again ;-)