Bernoulli Trials

Question

Assume that n = 10, and p = 7/10

Find the probability of at least 3 successes and at least 1 failure.

My work so far:

C(10,3) x 7/10³ x ???

I am not sure on what to do with the failure, I have never done a question with this included.

Thank you!!

Answer 1

Failure = 1 - probability of success.

Use this in your formula.

Answer 2

Hey Trinity. Hope you are doing well. I'd strongly recommend listing out the possibilities regarding the count of successes + failures that fit the criteria of "at least 3 successes and at least 1 failure". Since these possibilities cannot happen at the same time (eg: 1 success, 9 failures and 2 success, 8 failures cannot happen at the same time), you can add up the probabilities. Best of luck :)