### Brain Teasers

# Hats and Feathers

Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

You have five boxes with five hats in each and each hat has five feathers with five colored dots. Now the hats are in a rainbow of color and so are the feathers but the dots are all various random combinations of red, yellow, and blue-green.

What is the probability of getting a hat with only red dots?

What is the probability of getting a hat with only red dots?

### Hint

There are only 3 colors, blue-green is a single color.### Answer

ONE CHANCE in 33,891,544,377.72How did I get that answer?

The first thing we have to do is figure out how many different combinations of dots there are on a single feather. Since there are three colors possible for any given dot and five dots on a feather, you would multiply 3 to the fifth power. 3x3x3x3x3=243

So, you have a 1 in 243 possibility of a feather having solid red dots. You have 5 feathers on one hat, so you must take 1/243 to the 5th power.

1/243 x 1/243 x 1/243 x 1/243 x 1/243 = 1/847,288,609,443.

Now, working with the fact that you have 25 hats to work with (five boxes with five hats each), you must divide the 847+ billion chances by 25, or 847,288,609,443/25, which leaves you with one chance in 33,891,544,377.72.

In other words, not very likely.

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