# For a binomial random variable with n=5 and p=0.75:

# Pr(Y=3):

dbinom(3, 5, 0.75)


# Pr(Y <= 3):

pbinom(3, 5, 0.75)


# Pr(Y < 3) = Pr(Y <= 2):

pbinom(2, 5, 0.75) 

# Pr(Y > 3) = 1 - Pr(Y <= 3):

1 - pbinom(3, 5, 0.75) 

# Pr(2 <= Y <= 4) = Pr(Y <= 4) - Pr(Y <= 1):

pbinom(4, 5, 0.75) - pbinom(1, 5, 0.75)