Time for a Pop Quiz

Reply #5

Orange71 — Fri, 23 May 2025 21:29:34 GMT

Tucker, yes, you're right, that equation had an error. Should be j instead of m inside the outer sum.

Reply #4

Tucker Black — Fri, 23 May 2025 17:17:48 GMT

I don't think that is right. The first sum has j going from m to n, but there is no mention of j within that sum.

Reply #3

Orange71 — Fri, 23 May 2025 01:39:15 GMT

If Beavis only had to answer at least 7 out of 10 questions correctly, the probability would be only 1 in about 12688.

Here is the general equation for probability of at least m matches out of n

Reply #2

Orange71 — Thu, 22 May 2025 23:51:30 GMT

Tucker, you are on a roll my friend. You nailed the correct answer again !

As an aside, I made up this question in my head. I then ran it through AI apps (verbatim as posted here). ChatGPT got the wrong answer. Microsoft Co-pilot Quick Answer (2-3 second) option also got it wrong, but Think Deeper (~30 second) option resulted in the correct answer.

I myself was surprised by the degree of the improbability of the outcome until I did the calculations.

Reply #1

Tucker Black — Thu, 22 May 2025 02:55:39 GMT

I think I got this. I can't think of a less difficult way.

To get at least 14 questions right, Beavis has to get 14, 15, 16, 17, 18 or 20 questions right. He can't get 19 questions right because getting 19 of 20 right means the 20th question must be right.

There are 20! different ways to arrange the 20 unique answers. 20!=20*19*18*...*3*2*1=a huge number, approximately 2.4 million times a trillion. Only one of those ways results in getting all 20 questions right.

To get 18 right and... [ More ]

Time for a Pop Quiz

Orange71 — Tue, 20 May 2025 15:42:00 GMT

A school teacher completes a lesson on a subject, and the next day the teacher gives the class a pop quiz based on the lesson content. The quiz lists 20 questions, all of which have unique correct answers, and as the teacher is feeling generous, she decides to give the class some hints at the bottom of the quiz by listing all the (unique) answers, but in a random order relative to the order of the questions.

One of the students, Beavis, was not paying attention to the lesson and has no aptit... [ More ]