# Probabilities involving disjoint events

#### williamrobertsuk

##### New member
Find the problem attached!

Last edited by a moderator:

#### Dr.Peterson

##### Elite Member
Have you tried anything?

I would first try using De Morgan's laws to simplify $$\displaystyle A\cup(B^c\cap C^c)^c$$. 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

##### Elite Member
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. $$\displaystyle {\left( {{A^c} \cap \left( {{B^c} \cup {C^c}} \right)} \right)^c} = A \cup {\left( {{B^c} \cup {C^c}} \right)^c}$$