So I got this question on an practice test, and my first thought was to use Bernouilli's trial to solve for the answer. My question is how to possibly solve it without Bernouilli's trial, in a manner simply using conditional probabilities. I don't really know how to approach it in that case, however I figure it has to be extremely simple.
Customers at a store independently decide whether to pay by credit card or with cash. Suppose the probability is 70% that a customer pays by card. Find the probability that 3 out of 5 customers pay by card.
$p = 0.7$, and $q = 1 - p = 1 - 0.7 = 0.3$. Thus:
$P(x = 3) = \binom{5}{3}(0.7)^3\cdot (0.3)^2 = 0.3087 \approx 0.3$