Probabilities involving disjoint events

williamrobertsuk

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May 18, 2019
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Find the problem attached! :)

Capture3.JPG
 
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Dr.Peterson

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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

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Jan 29, 2005
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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. \(\displaystyle {\left( {{A^c} \cap \left( {{B^c} \cup {C^c}} \right)} \right)^c} = A \cup {\left( {{B^c} \cup {C^c}} \right)^c}\)
 
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