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most confusing number property problem!

Problem Solving — algebra and arithmetic
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by abcdefg » Sat Jun 13, 2009 11:27 am
This is found in p. 120 of the GMAT Review OG 11th edition.
P(A) = 0.23 and P(C) = 0.85

The book then jumps to the following conclusions.
1. We cannot determine P(A or C) and P(A and C)
2. 0.85 < P (A or C) < 1 [all inclusive]
3. 0.08 < P (A and C) < 0.23 [ all inclusive]

Can someone please explain to me how the book arrived at these conclusions?

The book says that P(A) + P(C) = 1.08, which is greater than 1, and therefore cannot equal P(A or C). Why is that?
The book then says following that P (A and C) > 0.08 inclusive.

Anyways just very confused. Would appreciate any help. Thanks.
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Source: — Quantitative Reasoning |
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by raleigh » Sat Jun 13, 2009 12:37 pm
Can you state the actual problem? I have OG 12th edition so I can't see the problem.
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by zenithexe » Sun Jun 21, 2009 4:04 am
Hey, I know it's old post, but I got OG 11th so here I go

this is not a problem question, he is confused about the explanation given regarding the "Discrete probability."
First part of his post is not really relevant, to boil it down, his question would be
Q1:Why is Event A and C cannot be mutually exclusive when P(A)+P(C)>1?

Q2:Why is P(A&C) >= 0.08 when P(A)+P(C)=1.08?


To explain, think of venn diagram with two circles. The area/probability of two circles minus the overlapping part must add up to less than 1.
Mutually exclusive means that two circles cannot overlap, hence, probability of A plus B must be less than 1. So, A and C cannot be mutually exclusive.

To make to the two circle's area to be less than 1, it has to overlap by 0.08 or grater to make the circle fit in a box with area of 1. If the overlap is grater than 0.08, then it will leave empty space in the box (probability of both events not occurring)

Look here for visualization: https://cs.uni.edu/~campbell/stat/venn.html
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