You have inherited an ice cream truck for the summer of 2022. You will be

selling ice cream from the truck every day that summer: 101 days in total, from Memorial Day

weekend until Labor Day weekend. This problem will step you through projecting how much ice

cream you expect to sell (as well as how much revenue you expect to make) during the summer.

a) Ice cream sales are known to be very dependent on weather. Suppose that for any

particular day, the weather is either rainy or sunny; on average, one-third of the days are

rainy and two-thirds of the days are sunny. Compute the expected number of sunny days

in Summer 2022 and the probability of there being more rainy days than sunny days in

Summer 2022. You may assume that the weather is independent between days.

b)It is more realistic to think that tomorrow's weather depends on today's weather

(for all days throughout the summer). Suppose that if it is sunny today, there is an 80%

chance that tomorrow will also be sunny; however, if it is rainy today, there is only a 30%

chance that tomorrow will be sunny. Additionally, suppose that the weather on 'Day 0' (i.e.,

the day before your ice cream truck opens) is known to be sunny.

Based on a simulation with 10,000 replicates, estimate the probability of there being more

rainy days than sunny days in Summer 2022. Write a brief paragraph outlining the logic of

the simulation and clearly comment your code