# Probability of Snow On Friday, But Not Saturday

Suppose there is a $$50$$ percent chance it snows on Friday, $$60$$ percent chance it snows on Saturday, and $$40$$ percent chance it snows on both days. What is the probability that it snows on Friday, but not Saturday?

I have the following, but am not sure if it is correct:

$$\textbf{Let:}$$

• $$F =$$ Event that it snows on Friday
• $$S =$$ Event that it snows on Saturday

$$\textbf{Want: }$$

• $$P(FS^c)\\$$

$$\textbf{My Solution:}\\ P(FS^c) = P(S^c|F)P(F) = (0.4)(0.6)?$$

The main problem I run into is if I used the correct value for $$P(S^c|F)$$. I got $$0.4$$ from the the fact that it does not rain on Saturday $$100(1 - 0.6) = 40$$ percent of the time. Should I be utilizing the fact that it rains on either day $$60$$ percent of the time, or did I approach the solution from the wrong angle?

• $0.4=P(F\cap S)=P(F)\cdot P(S|F)=0.5\cdot 0.8\ne 0.3=0.5\cdot 0.6=P(F)\cdot P(S) \Rightarrow P(S|F)\ne P(S) \\ \text{So,$F$and$S$are dependent}$. Feb 3, 2019 at 9:58

To solve the problem, you can use the following identity: $$P(FS^c)=P(F)-P(FS)$$
Note that $$P(S^c|F)=1-P(S|F) \ne 1-P(S)$$.
• Congratulations for the $101\,k$ reputation ! I am sorry to have missed the day on which you passed the $100$. Cheers. Feb 3, 2019 at 7:32