Solve the following problems using Monte Carlo simulation. If you can think of a way to compute it with permutations or with a direct analysis, do that, too!
Problem 1: In the city of Bangalore the probabilty of rain on any given day is 29%. What is the probability that it will rain on exactly 4 days in a given week?
Problem 2: Two couples and one single person are seated at random in a row of five chairs. What is the probability that neither of the couples sits together in adjacent chairs?
Problem 3: A fair coin is tossed 5 times. What is the probability of getting heads on three or more consecutive tosses?
Problem 4: If you roll two dice repeatedly, what is the probability of rolling a sum of 4 before rolling a sum of 7?
Problem 5: Students in a class are selected at random, one after the other, from a class consisting of 7 boys and 8 girls. What is the probability that boys and girls in the class alternate starting with a girl first?
Problem 6: A white urn contains 10 white marbles and a black urn contains 10 black marbles. First, a marble is selected from the white urn and placed in the black urn. Then, a marble is selected at random from the black urn and placed in the white urn. Finally, a marble is selected at random from the white urn. What is the probability that the marble selected is white?