really in need of help to try to figure this problem out.

What kind of help do you need? Where are you stuck? Can we see your work for A, C and E so we can see the method you like to use?
 
i have gotten A, C, E so far.
Do you mean "a, c, e"? A and C are sets and the is no "E".
What did you get for a, c, and e?

This is really just a matter of understanding what the Venn diagram represents.
(b) asks for \(\displaystyle P(B\cap A)\). That is the area where sets A and B overlap (ignoring set C). There is nothing in that region so \(\displaystyle P(B\cap A)= 0\).

(d) asks for the probability of the complement of C- everything that isn't in C. C consists of points 2, 5, and 6. Everything else, 1, 3, and 4, are not in C. We are told that P(1)= 0.3 and that P(3) and P(4) are both 0.1. So P(C)= 0.3+ 0.1+ 0.1= 0.5.

(f) is just a matter of knowing what "mutually exclusive" means! Two sets (or events) are "mutually exclusive" if they are completely separate (disjoint)- that they have nothing in common. I see that point 5 lies in both A and C.
 
Do you mean "a, c, e"? A and C are sets and the is no "E".
What did you get for a, c, and e?

This is really just a matter of understanding what the Venn diagram represents.
(b) asks for \(\displaystyle P(B\cap A)\). That is the area where sets A and B overlap (ignoring set C). There is nothing in that region so \(\displaystyle P(B\cap A)= 0\).

(d) asks for the probability of the complement of C- everything that isn't in C. C consists of points 2, 5, and 6. Everything else, 1, 3, and 4, are not in C. We are told that P(1)= 0.3 and that P(3) and P(4) are both 0.1. So P(C)= 0.3+ 0.1+ 0.1= 0.5.

(f) is just a matter of knowing what "mutually exclusive" means! Two sets (or events) are "mutually exclusive" if they are completely separate (disjoint)- that they have nothing in common. I see that point 5 lies in both A and C.

for a) i got = 0.5
c) = 1.0
e)= 0.4 are those correct
 
for a) i got = 0.5
c) = 1.0
e)= 0.4 are those correct
Yes, (a) asks for P(A). A contains points 1, 3, and 5. P(1)= 0.3 while P(3) and P(5) are both 0.1. P(A)= 0.3+ 0.1+ 0.1= 0.5.

Yes, (c) asks for \(\displaystyle P(A\cup B\cup C)\). That is everything! Of course they all add up to 1.0. \(\displaystyle P(A\cup B\cup C)= 1.0\).

There are two things marked "e"! The first asks for \(\displaystyle P(A\cap C')\). C' is standard notation for the complement of C- everything that is not in C. Points 1, 3, and 5 are in A. Point 5 is also in C while points 1 and 3 are not. Yes, \(\displaystyle P(A\cap C')= P(1)+ P(3)= 0.3+ 0.1= 0.4\).

The other "e" asks for \(\displaystyle P(B|A)\). "B|A" is "in B given that it is in A" so, in this case, that is the same as \(\displaystyle B\cap A\). That is the same as (b). \(\displaystyle P(B|A)= P(B\cap A)= 0.0\)
 
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