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Let S be a set of outcomes and let A and B be events with outcomes in

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dave13
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Let S be a set of outcomes and let A and B be events with outcomes in [#permalink] New post   25 Jun 2021, 01:17
VeritasKarishma wrote:
gmatt1476 wrote:
Let S be a set of outcomes and let A and B be events with outcomes in S. Let ∼B denote the set of all outcomes in S that are not in B and let P(A) denote the probability that event A occurs. What is the value of P(A) ?

(1) P(A ⋃ B) = 0.7
(2) P(A ⋃∼B) = 0.9


DS95491.01


Consider the set S (the rectangle). A and B are subsets in it. They may have some overlap.
We need A which is shown by yellow + green.
Attachment:
Screenshot 2021-06-25 at 10.18.44.png


(1) P(A ⋃ B) = 0.7
This means the yellow + green + blue = 0.7
We need yellow + green. Not sufficient

(2) P(A ⋃∼B) = 0.9
This means yellow + green + white = 0.9
(because we need any element which is either in A (so all elements of A work) or not in B (all white elements) or both (it is in A but not in B). We need yellow + green. Not sufficient.

Using both,
yellow + green + blue + yellow + green +white = 0.7 + 0.9 = 1.6

Now note that
yellow + green + blue + white = 1

So yellow + green + 1 = 1.6
yellow + green = 0.6
Sufficient
Answer (C)

Also Check: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/0 ... s-of-sets/

Bambi2021



VeritasKarishma thanks. here is the problem i still dont get.

you say "You are right.
P(A U B) = P(A) + P(B) - P(Both)"

but in ST 1 you still add BOTH instead of P(A U B) = yellow +blue - green = 0.7

pls explain the paradox :grin:

or maybe P(A U B) means either A or B or Both A and B then what is the point .....
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dhawalsachdeva
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Re: Let S be a set of outcomes and let A and B be events with outcomes in [#permalink] New post   27 Jun 2021, 12:03
P(A U B) = P(A) + P(B) - P(Both)

Per the statement 1 i.e.P(A U B) =0.7, we cannot infer anything for P(A) after using the above formula.

Similarly per the statement two we cannot infer anything for P(A) too.

Now we add both statements we get,

P(A U B) + P(A U ~B) = 1.6
Expanding the expression,

P(A) + P(B) - P (A both B) + P(A) +P(~B) - P (A and ~B) = 1.6

2*P(A) + 1 - P (A) = 1.6 [SINCE P(B)+P(~B) = 1 and P (A both B) +
P (A both ~B) = P(A)]

P(A) = 0.6, so OA is C.

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prathinmba
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Re: Let S be a set of outcomes and let A and B be events with outcomes in [#permalink] New post   04 Aug 2021, 16:21
Since the question doesn't state whether these are independent events or dependent, isn't the data in options 1 and 2 given insufficient?
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gmatbyexample
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Re: Let S be a set of outcomes and let A and B be events with outcomes in [#permalink] New post   27 Nov 2021, 09:02
Expert Reply
prathinmba wrote:
Since the question doesn't state whether these are independent events or dependent, isn't the data in options 1 and 2 given insufficient?


Could you elaborate on this?
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Re: Let S be a set of outcomes and let A and B be events with outcomes in [#permalink] New post   07 Dec 2023, 07:41
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Re: Let S be a set of outcomes and let A and B be events with outcomes in [#permalink]
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