The Law of Large Numbers is an important result from probability theory that describes the outcome of repeating an experiment a large number of times. In this talk, we identify the set of all infinite sequences of coin tosses, B, with the half open unit interval. From there we will look at how we can use some basic facts in measure theory and the Borel principle to calculate the probabilities of events in B. We will define the Rademacher functions and then prove a special case of Chebyshev’s inequality involving nonnegative, piecewise constant functions. These tools are then used to provide a proof for the Weak Law of Large Numbers for infinite sequences of coin tosses.