## Archive for September 4, 2010

### The Perfect Pack – My Solution

Here’s a question I posted a few days ago:

A standard pack of M&M’s contains pieces of six different colors. What is the probability that there will be an even number of M&M’s of each of the six colors?

As far as I’m concerned, the type of pack you select is irrelevant, as is the proportion of the colors within the pack. Even though MARS^{®} claims a certain proportion for the mixtures at the factory, the proportion of colors varies from bag to bag. Therefore, my solution is independent of the number of M&M’s.

For each color, the number of M&M’s will be either even or odd. Consequently, the probability of having an even number of one specific color is 1/2. Since there are six different colors, then the combined probability of having an even number of every color is (1/2)^{6} = **1/64**.

I’ve eaten way more than 64 packs of M&M’s in my life, so I’m surprised that I’ve never encountered a “perfect pack.”