Alice and Bob have 2𝑛 + 1 coins, each with probability of a head equal to 1/2. Bob tosses 𝑛 + 1 coins, while Alice tosses the remaining 𝑛 coins. Assuming independent coin tosses, show that the probability that after all the coins have been tossed, Bob will have gotten more heads than Alice, is 1/2. Write a program, in any language, that simulates this experiment with 𝑛 equal to 300. Perform 1000 trials of this experiment, and compute the relative frequency of Bob tossing more heads than Alice. relative frequency = number of trials in which Bob tossed more heads total number of trials Note this relative frequency is an approximation to 𝑃(Bob tosses heads more than Alice). Verify that your relative frequency is very close to 1/2. Now suppose that we do another sequence of 1000 trials with 2𝑛 + 1 loaded coins (again 𝑛 = 300). In particular, run all 1000 trials of the experiment, but now with the probability of heads equal to 𝑝. Do this for each 𝑝 ∈ {0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8}