SOLUTION: A sample space contains 7 sample points or outcomes. Let events and be defined according to the Venn diagram below. Let: P(1) = P(2) = P(3) = P(7) = 0.1, P(4) = P(5) = 0.05.

Question 1206166: A sample space contains 7 sample points or outcomes. Let events and be defined according to the Venn diagram below.
Let:
P(1) = P(2) = P(3) = P(7) = 0.1,
P(4) = P(5) = 0.05.
and P(6) = 0.5.

P(AUB) =
(b) P(4) =
(c) P(An B) =
(d) P(AUA) =
A=1,5,6
B=4,7
A/B=2,3
Found 3 solutions by ikleyn, greenestamps, mccravyedwin:
Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.

What is given in this post, are the numbers, but not a Venn diagram.

Venn diagram is not shown.

As presented in this post, the problem can not be solved. Naturally.

Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

You are not going to get useful responses to your posts if you don't present the problems clearly....

The meaning of "Let events and be defined..." is unclear; possibly you used some symbols that did not survive the trip to this site.

The 7 given probabilities add to 1, so we can guess that the outcomes are mutually exclusive.

Beyond that, we really have to guess what is going on.

Given "A=1,5,6" and "B=4,7", we can guess that "P(AUB)" is P(1)+P(5)+P(6)+P(4)+P(7)....

But the meaning of "A/B=2,3" is a complete mystery.

Re-post your problem clearly if you want help with it....

Answer by mccravyedwin(406)   (Show Source): You can put this solution on YOUR website!

I'm trying to guess what you meant. I'm guessing you had 3 overlapping sets (circles), labeled A,B,C with 7 regions numbered 1 to 7. P(A∪B) = P(1) + P(4) + P(2) + P(5) + P(3) + P(6) = 0.1 + 0.05 + 0.1 + 0.05 + 0.1 + 0.5 = 0.9 P(4) = 0.05 (That's given above. Don't know why they would ask that!!!) P(A∩B) = P(2) + P(5) = 0.1 + 0.05 = 0.15 P(A∪A) = P(A) = P(1) + P(2) + P(4) + P(5) = 0.1 + 0.1 + 0.05 + 0.05 = 0.3 ------------------------------------------------------------ I have no idea what the rest of what you wrote meant. I can't even guess. A=1,5,6 but A isn't those regions! B=4,7 but B isn't those regions! A/B=2,3 Is that the difference of A minus B? If so that is not 2,3. Sorry, We have no idea of what that could mean. Edwin

RELATED QUESTIONS
The accompanying Venn diagram illustrates a sample space containing six sample points and (answered by MathLover1,Edwin McCravy)
Let A and B be events in a sample space S such that P(A) = 0.6, P(B) = 0.4, and P(A... (answered by jim_thompson5910)
Let A and B be two events in a sample space S such that P(A) = 0.6, P(B) = 0.4, and P(A... (answered by stanbon)
Find the following probabilities: (A) Events A and B are mutually exclusive events... (answered by stanbon)
Let A and B be events in a sample space S. If P(A)= 2/9, P(B)= 7/36, and P (A and B)=0,... (answered by ikleyn,greenestamps)
Two dice both four sided and fair are rolled simultaneously and the product of the two... (answered by Boreal)
A lottery ticket has a color: Red or Blue followed by one number among 1, 2 and 7. (a)... (answered by stanbon)
A and B are events in a sample space S such that P(A) = 0.41, P(B) = 0.31 and P(A and B)... (answered by ikleyn)
The accompanying Venn diagram illustrates a sample space containing six sample points and (answered by ikleyn)