After arriving on your vacation in Hawaii you learn that the

After arriving on your vacation in Hawaii, you learn that the local weather service forecasts a 60% chance of rain every day this week. Estimate the probability of 3 consecutive rainy days this week by using 1 million Monte Carlo simulations. Now assume that if today is rainy, there is a 75% chance that tomorrow will be rainy, and likewise if today is sunny, there is a 75% chance that tomorrow will be sunny. The day you arrived on your vacation was sunny. Estimate again the probability of 3 consecutive rainy days in the week using 1 million Monte Carlo simulations.

Solution

a)

probability of 3 consecutives rainy days = 0.60 * 0.60 * 0.60 = 0.216

b)

Probability of 3 consecutives rainy days = 0.75 * 0.75 * 0.75 = 0.421875