Question

Your box of cereal may be a contest winner! It's rattling, which 100% of winning boxes do. Of course 1% of all boxes rattle and only one box in a million is a winner. What is the probability that your box is a winner? Please specify your answer as a probability (i.e. .05 rather than 5%).

Answer 1

Just take 1% of 1 million since you already know you're in the 1% since your box is rattling:
\[0.01*1,000,000=10,000\]So that would be 1 in 10,000 which can also be expressed as:\[\frac{1}{10000}=0.0001\text{%}\]

Answer 2

Here is the theory behind it:
http://en.wikipedia.org/wiki/Bayes'_theorem#Introductory_example

Answer 3

Correct answer is 0.0001 or 0.01%

Answer 4

Yea...I mistakenly added the % sign at the end when I hadn't converted it to a %. Good catch.