If the event A is the event, {I am leaving work early today}, and B is the event, {there is a football game that I want to watch}. Given the following joint probabilities:
p(I am leaving work early, there is a football game that I want to watch this afternoon) = .1
p(I am leaving work early, there is not a football game that I want to watch this afternoon) = .05.
p(I am not leaving work early, there is not a football game that I want to watch this afternoon) = .65
How do I go about finding the probability B, that there is a football game that I want to watch this afternoon?
\begin{align*} P(B)&=1-P(B^c)\\ &=1-P((A\cap B^c) \cup (A^c\cap B^c))\\ &=1-P(A\cap B^c)-P(A^c\cap B^c)\\ &=1-0.05-0.65\\ &=0.3 \end{align*}