at most, at least, exactly...geometric probability & binomial probability

For example, I have a problem in my book, the probability of school having a contract is 0.62, and you have a random sample of 20 schools.

Whats probability at least 4 schools w/ contract?

Whats probability between 4 and 12 schools w/ contract?

Whats probability at most 4 schools w/ contract?

You don't have to answer the question...just maybe clarify:

if the problem says "at least" then p(none)-p(1)? wait I think this is wrong...oh and calculator keystrokes would be great btw...like binomcdf(...)

Basically just walk me through, any help is greatly appreciated

Re: at most, at least, exactly...geometric probability & binomial probability

P(at least 4 schools w/contract) is the same as 1 minus P( 0, 1, 2, 3 schools have contract)

2nd question I will leave alone for now, maybe after this post you will see how to solve

P(at most 4 schools w/contract) = P(0,1,2,3,4 schools have contract).

I will never give you keystrokes because 1) I dont own such calculators and couldnt tell you if I wanted to; and 2) I wouldn't tell you if I could, it would defeat the purpose for learning which I hope is the goal you seek (rather than the solution to to the problem per se)

I am happy to walk you through further if you want to learn rather than get answer to problem