A 7.8 km canal passes through the city for skating. It takes 10 to 14 days of continuous temperature (-15 degree celsius or colder) to form ice, which allows for skating. Data from the past 40 years shows that, during the 120 days of winter season, on average, the canal was open for skating for 50 days, and the weather was sunny for 54 days. On average, a winter season would have 33 sunny days when the canal is open for skating. What is the probability that on a randomly chosen day during the winter season, the canal is open for public skating, but the weather is not sunny?
Let's call the event when canal is open `C` and event when day is sunny `S` .
Out of 50 days of open canal and 54 sunny days 33 coincide. Hence conditional probability that the day is sunny when the canal is open is `P(S|C)=33/50=0.66` hence the probability that canal is open but day is not sunny is `P(barS|C)=1-0.66=0.33.` ` `
`barS` means not sunny.
And probability that the canal is open is `P(C)=50/120=5/12`
(50 out of 120 days of the winter season).
So the probability that on a randomly chosen day during the winter season the canal is open and day is not sunny is `P(C)P(barS|C)=11/80=0.1375`