Help with probability

Jeonsah

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Feb 5, 2012
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Hi guys. I am currently needing help with some probability and stats questions. For some reason I understand the lectures but I am unable to figure out any of the problems in the book. I have stared at these problems for hours and I just dont get them. So im in dire need of help. Once I get the hang of them, i should be ok. Here are a couple of the problems I am having a hard time with:

Let E, F, G be three events. Find expressions for the events that of E,F,G.
a. at least two of the events occur
b. none of the events occur
c. exactly two of them occur
d. at most three of them occur


I am unsure of how to express these. I dont know where to start at all. If anyone can help me that would be greatly appreciated.

The other problem I am having trouble with is this:

Show that if E is subset of F then P(E) <= P(F). (Hint: Write F as the union of two mutually exclusive events, one of them being E.)




Thank you!
 
Let E, F, G be three events. Find expressions for the events that of E,F,G.
a. at least two of the events occur

Show that if E is subset of F then P(E) <= P(F). (Hint: Write F as the union of two mutually exclusive events, one of them being E.)
If is hopeless to try to study probability if one does have a through grounding in set theory.

a) \(\displaystyle (E\cap F)\cup (E\cap G)\cup (G\cap F) \).

2) \(\displaystyle F=(F\cap E^c)\cup E\)
 
Hello, Jeonsah!

I don't know what your teacher or textbook wants for answers.


Let E, F, G be three events.

Find expressions for the following events.

(a) at least two of the events occur.

\(\displaystyle (E \wedge F)\,\vee\,(F \wedge G)\,\vee(E \wedge G)\,\vee (E \wedge F \wedge G)\)


(b) none of the events occur.

\(\displaystyle (\sim\!E) \,\wedge (\sim\!F) \,\wedge (\sim\!G)\)


(c) exactly two of them occur.

\(\displaystyle (E \wedge F)\,\vee\,(F \wedge G) \,\vee\,(E \wedge G)\)


(d) at most three of them occur.

\(\displaystyle E \vee F \vee G\)
 
Surely \(\displaystyle (E\cap F)\cup(E\cap G)\cup(G\cap F)\) also includes \(\displaystyle (E\cap F\cap G)\).

Moreover, exactly two is:
\(\displaystyle (E\cap F\cap G^c)\cup(E\cap F^c\cap G)\cup(E^c\cap F\cap G)\)
 
Thank you for the help guys! I am slowly starting to figure this out now. I understand the lectures but I just cant get my foot in on any of the problems from the book. Thank you!
 
Prob and Stats for Engineers. I really have a hard time transitioning from the teacher's lectures(i understand them) to the practice problems. Im working on them though. Thanks for the help again guys!
 
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