====== Math 445 Lab 7: Computing probabilities with Monte Carlo simulation ======

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?

  * 1/5
  * 1/4
  * 3/8
  * 2/5
  * 1/2

**Problem 3:** A fair coin is tossed 5 times. What is the probability of getting heads on three or more consecutive tosses?

  * 2/16
  * 1/4
  * 7/24
  * 5/16
  *15/32

**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?