Starbursts + Math = Fun

Most people just eat the candy. Me? I do the math.

Explanation: Not so long ago, I was eating from a box of Starbursts. While not a huge fan of candy, I seem to have a bit of a weakness for their chewy goodness. Anyway, the Starbursts were individually wrapped and inside a box, so I could reach in and just grab a bunch. My normal Starburst eating style is to grab 4 or 5, vow that I'll stop after those, and repeat until the box is empty.

At one point, I took 4 Starbursts out and they were all red. As the red ones are my favorites, I didn't have much of a complaint, but I did notice how unusual it seemed that all four were red. Most people would stop there, but me? I did the math.

Embarrassingly, I had to look to see how many varieties of Starburst were in the box. The answer was five: red, pink, yellow, orange, and green. Furthermore, I assumed that I would have been impressed to pick any four of the same color, not just reds. That means the probability of this occurrence was really just the probability that I picked four Starbursts, where the color of one didn't matter and the color of the other three were the same as the first.*

From there, the math was straightforward. Five to the third power is 125, so the probability was 1/125, or 0.8%. Not inconceivable odds, but not very likely either. I then ate my little math project.

*People tend not to consider this assumption, but it is quite important. For instance, you may look at a family with four daughters and say that it's amazing because the probability that all four children were girls is 1/16, or 6.25%. In reality, though, you would have thought the same thing about four boys. The probability you would be computing is NOT the probability that there would be four girls, it's the probability that you'd be amazed by the genders of the four children. The probability that four kids are all the same sex is just 1/8 or 12.5%. I once demonstrated this to somebody by flipping a coin three times. The coin came up heads all three times. Admittedly, my demonstration could have gone worse, but luckily, it was a friendly coin.**

**Yes, I just said "luckily" in a post about probability. Deal with it.