1. ## Probabilities

You have a quiz with 5 questions.
They are multiple choice with 4 possible answers for each question.

You guess on all of them.

1. Whats the probability you get them all wrong?
2. Whats the probability you get them all right?
3. Whats the probability you get at least one right?

2. Originally Posted by Morgan82
You have a quiz with 5 questions.
They are multiple choice with 4 possible answers for each question.

You guess on all of them.

1. Whats the probability you get them all wrong?
2. Whats the probability you get them all right?
3. Whats the probability you get at least one right?
$\displaystyle P(\text{correct}) = \frac{1}{4}$
$\displaystyle P(\text{incorrect}) = \frac{3}{4}$

1. $\displaystyle P(\text{incorrect})^5 = \frac{243}{1024}$

2. $\displaystyle P(\text{correct})^5 = \frac{1}{1024}$

3. $\displaystyle P(\text{at least one correct})$ $\displaystyle = 1 - P(\text{all incorrect})$ $\displaystyle \Rightarrow 1 - P(\text{incorrect})^5 = \frac{781}{1024}$

3. Originally Posted by Plato
Recall that at least one is the opposite of none.
I tend to write in pure math, but this is the reasoning why it looked so easy!