For this lab, we will run some simulations of rolling dice and tossing coins using the statistical software program R. Your solutions should contain clearly identified numerical answers and well labeled tables/figures, where appropriate. Make sure to include clear and concise interpretations (that is, clear full sentences) of any values, figures, and responses to queries posed. Place all code in an appendix, at the end of your solutions document.
1) Simulate the probability that a random integer between 1 and 5000 is divisible by 4, 7, or 10.
a) Run this simulation for 10, 100, 500, and 1,000 trials
b) For each simulation in a), calculate the estimated proportion of this event for each simulation
2) A 20-sided DnD die is tossed ten times
a) Calculate by hand the theoretical probability of rolling at least one 15 in ten tosses
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b) Simulate and estimate the probability of obtaining at least one 15 when tossing a 20-sided DnD die ten times for 1,000 trials
c) Compare the theoretical probability from (a) with your empirical proportion from (b)
