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?
To solve the problem, you can use the following identity: $$P(FS^c)=P(F)-P(FS)$$