I'm stumbling on what I think is just a simple problem but am a bit out of practice (out of school for 30 years and attempting to relearn some old stat information):
Two independent binomial distributions as follows: A: Binomial N = 10, p=70% B: Binomial N = 10, p=20%
What is the probability of B >= A given than B is equal to 5? I've started by attempting to solve for the probability of B >= A and B = 5 over probability that B = 5. Denominator is straight forward but I am struggling to take the appropriate next steps on the numerator. My text only has the question and numeric solution and I'm unable to match the answer. Since B is given to equal 5, isn't my numerator simply the probability that A is <= 5? Thanks for any assistance.