The probability that at least one of the two customers buys a banana is 55/64
How to determine the required probability
From the question, we have the following parameters that can be used in our computation:
The tree diagram
The probability that at least one of the two customers buys a banana is
P(At least one) = 1 - P(None)
From the tree diagram, we have
P(None) = P(Cookie) * P(Cookie)
P(None) = 3/8 * 3/8
P(None) = 9/64
So, we have
P(At least one) = 1 - 9/64
P(At least one) = 55/64
Hence, the probability is 55/64