Using regular vs. conditional probability - when is it appropriate in this case?

Question

I'm working on the following problem:

Jerry and Susan have a joint bank account. Jerry visits the bank 20% of the days, while Susan goes there 30% of the days. Together, they are at the bank 8% of the days. Susan was at the bank last Monday. What is the probability that Jerry was there, too?

I thought that the question was easy enough, the probability that both of them were at the bank at the same day is 8%. However, solutions I've found online use conditional probability instead, and have ~26% as the answer. I understand that conditional probability is used to reason about the probability of events using partial information, but in this case it strikes me as inappropriate to utilize? How is this correct?

Answer 1

We're given $P(\text{Jerry})=0.2$, $P(\text{Susan})=0.3$, and $P(\text{Jerry}\cap\text{Susan})=0.08$.

Then by definition of conditional probability,

$$P(\text{Jerry}\mid\text{Susan})=\frac{P(\text{Jerry}\cap\text{Susan})}{P(\text{Susan})}=\frac{0.08}{0.3}=0.2666\ldots$$

Use conditional probability here because we know Susan's at the bank on Monday; knowing this, we want to know the probability Jerry was, too.

Answer 2

It is apropriate because what you have is exactly "partial information". You know that she was there, but you're not sure about him.