Probabilities involving disjoint events

[williamrobertsuk]

Find the problem attached!

 

[Dr.Peterson]

Have you tried anything?

I would first try using De Morgan's laws to simplify [MATH]A\cup(B^c\cap C^c)^c[/MATH]. Then question 1 will be fairly easy.

Please show us your work, and ask any specific questions it raises. Also, please reread the submission guidelines.

 

[pka]

Find the problem attached!

View attachment 12190

Here are HINTS only. You must apply them and post results.
For 1. $\displaystyle {\left( {{B^c} \cup {C^c}} \right)^c} = B \cap C$

For 2. If $\displaystyle H~\&~G$ are disjoint events then $\displaystyle \mathcal{P}(H\cup G)=\mathcal{P}(H)+\mathcal{P}(G)$

For 3. $\displaystyle {\left( {{A^c} \cap \left( {{B^c} \cup {C^c}} \right)} \right)^c} = A \cup {\left( {{B^c} \cup {C^c}} \right)^c}$