1. Independant events

The probability of Faye attending the gym on a given day is 0.6

The probability of Karen attending the gym on a given day is 0.85

Find the probability that one of the two attend.

Do I use $P(F\cup K)=P(F)+P(K)-P(F\cap K)$ ?

2. That's correct, provided that by "one of the two attend" you mean at least one attends (instead of exactly one).

You will need to make an assumption that the events of their attending are independent. Ideally, that would be part of the problem statement.

3. Originally Posted by awkward
That's correct, provided that by "one of the two attend" you mean at least one attends (instead of exactly one).
I am told the events are independant.

How would I solve it for "exactly one"?

4. The probability that exactly one attends is

$P(F \cap K^c) + P(F^c \cap K)$.