Problem 2: Binomial distribution

Determine the following probabilities using base R function (i.e. not through approximation).

a) I ask my dog Barbara to sit like a good boi 15 times. Each time I ask him, he either sits or does not sit. From experience I know that he will sit 4 out of 5 times whenever I ask him. What is the probability that he will sit down every time I ask him?

b) We are all praying for rain in Santa Barbara but we also hope that it does not rain too much. So we want to find out what the probability is for the perfect number of rainy days in the month of January. In the month of January, the probability of having a rainy day is 0.16. What are the chances that I observe between 3 and 8 days of rain? For this question, assume that on any given day it either rains or it doesn't rain (the amount of rain is irrelevant for this question).

please solve both the parts as required in the question