Question

A multiple choice quiz has 8 questions each with 4 possible answers, but only 1 is correct. If a student randomly guesses on each question, what is the probability of getting the first 4 questions correct? :) ​

Answer 1

Answer:

First, we ignore the final 8 questions, nobody is asking about those.

So there are 4 questions with 4 answers each.

There is 1 way to get all four answers correct.

There are 4^4 possible combinations of answers

Simple probability is found by dividing the count of ways to fit requirements by the count of possible results.

1/4^4.

That’s also 1/256

Another way to do this is to realize there’s a 1/4 chance of a correct answer, and only if you get the first question right do you care that there’s a 1/4 chance of correct answer to the second, making it 1/4*1/4 chance of the first two in a row being right.

Similarly, the chance of the three in a row is 1/4*1/4*1/4 and the chance of four in a row is then 1/4*1/4*1/4*1/4.

Of course that means 1^4/4^4

1^4 is just 1. 4^4 is 256

So we’re back at 1/256

hope this helps ❤