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  3. Monte Carlo Simulations in Python

Exercise

Betting between Tom and Eva

It's time to play a game between Tom and Eva!

Recall that Tom has a regular six-faced die and the results of rolling it follow a discrete uniform distribution in the interval of one and six. Eva has a biased coin that has a probability p of turning heads. The distribution of the number of flips Eva needs to land heads is geometric.

Here are the rules of the game:

  • Tom's score: the point of the rolled die
  • Eva's score: the number of flips needed to land heads
  • The person with the highest score wins

Your task is to simulate this game! For the list of possible p values [0.1, 0.2, 0.3, 0.5, 0.7, 0.8, 0.9] representing the probability of Eva's coin flipping heads, who do you expect to win?

NumPy has been imported as np and SciPy's stats module as st.

Instructions

100 XP
  • Simulate rolling Tom's die 10,000 times, assigning the results to die_samples.
  • Simulate Eva's coin flips to land heads 10,000 times, assigning the results to coin_samples.