Multiple Choice Quiz Probability Question!

[KingAce]

The question is as follows:

There are 5 MC questions on a quiz. Each question has four answers.
If you guess, what is the probability you'll get 4 out of 5 questions right?

I did actually get this wrong on a quiz (ironically) and I really want to know how to solve it. Thanks for your help!

 

[soroban]

Hello, KingAce!

This is a "binomial" probability.
I hope you're familiar with the formula.

There are 5 MC questions on a quiz. Each question has four answers.
If you guess, what is the probability you'll get 4 out of 5 questions right?

\(\displaystyle \text{The probabilities are: }\;\;P(\text{right}) \:=\:\frac{1}{4}\qquad P(\text{wrong}) \:=\:\frac{3}{4}\)

\(\displaystyle \text{The probability of getting 4 right and 1 wrong is: }\;{5\choose4}\left(\frac{1}{4}\right)^4\left(\frac{3}{4}\right) \;=\;\frac{15}{1024}\)