or each of the following problems, create a program that allows you to run the appropriate sim- ulation models. You may use whatever programming language you like

1.

2. Three points are chosen at random on the circumference of a circle. Estimate the probability that they all lie on the same semicircle, by Monte Carlo sampling methods. Perform 5 replications.

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4.

A baker is trying to figure out how many dozens of bagels to bake each day. The probability distribution of the number of bagel customers is as follows Number of Customers/Day 8 10 12 14 Probability 0.35 0.30 0.25 0.10 Customers order 1, 2, 3, or 4 dozen bagels according to the following probability distribution Number of Dozen Ordered/Customer 1 2 3 4 Probability Bagels sell for $8.40 per dozen. They cost $5.80 per dozen to make. All bagels not sold at the end of the day are sold at half-price to a local grocery store. Based on 5 days of simulation, how many dozen (to the nearest 5 dozen) bagels should be baked each day? 0.4 0.3 0.2 0.1