Roll Dice, Flip Coins

This question comes from Professor David Morin’s book, Probability For the Enthusiastic Beginner, Chapter 1, page 26.

1. One person rolls two six-sided dice, and another person flips six two-sided coins. Which setup has the larger number of possible outcomes, assuming that the order matters?

Imports

import itertools

Roll Two Six-Sided Dice

Create a list representing a six-sided die.

die = ['1','2','3','4','5','6']

If you prefer the statement “rolling two six-sided die once”, then create all possible outcomes of rolling two identical die, returning a Cartesian product of the list die and itself.

dice_permutations = list(itertools.product(die, die))

If you prefer the statement “rolling one six-sided die twice”, then create all possible outcomes using the repeat option.

dice_permutations = list(itertools.product(die, repeat=2))

Both return the same outcome.

list(itertools.product(die, die)) == list(itertools.product(die, repeat=2))

True

Flip Six Two-Sided Coins

Create a list representing the two outcomes of flipping a coin.

coin = ['H','T']

If you prefer the concept of flipping six two-sided coins, then list all six coins.

coin_permutations = list(itertools.product(coin, coin, coin, coin, coin, coin))

If you prefer of flipping one two-sided coin six times, then using the repeat option.

coin_permutations = list(itertools.product(coin, repeat=6))

Again, they’re identical.

list(itertools.product(coin, coin, coin, coin, coin, coin)) == list(itertools.product(coin, repeat=6))

True

Compare Possible Outcomes

Flipping six two-sided coins yields $2^6 = 60$ possible outcomes and rolling two six-sided dice yields $6^2 = 36$ possible outcomes. The power of exponential growth!

coin_permutations > dice_permutations

True