ATypically this is something done for factoring. To do that, I use trail and error. Do you need to do it by a system of equations?
Answer:
P(F | C) = 0.96
Step-by-step explanation:
Hi!
This is a problem on conditional probability. Lets call:
C = { cloudy day }
F = { foggy day }
Then F ∩ C = { cloudy and foggy day }
You are asked for P(F | C), the probability of a day being foggy given it is cloudy. By definition:

And the data you have is:

Then: P(F | C) = 0.96
Change the 15 1/3 to an improper fraction (46/3). Next multiply this by (3/4).
(46/3)(3/4) = 46/4 = 23/2 = 11.5 gallons was used to water the plants
15 1/3 - 11 1/2 = 46/3 - 23/2 = 92/6 - 69/6 = 23/6 = 3 5/6 gallons of water are left in the barrel