1. Suppose we have a die that has a 40% chance of coming up "red". We roll the die 12 times.
(a) Show that this situation meets the criteria for using the binomial distribution.
(b) How many ways are there to get exactly 5 red results in those 12 rolls?
(c) What is the probability of getting exactly 5 red results in those 12rolls?
(d) What is the probability of getting at least one red result in the 12?
(e) What is the probability of getting exactly 1 red result in the 12 rolls? (This is NOT the same question as (d))
(f) What is the expected number of red results in the 12 rolls?
(g) What is the standard deviation of the number of red results in the 12 rolls?
