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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Suppose A and B are two events that are not independent. Is the proba

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Math Expert V
Joined: 02 Sep 2009
Posts: 58445
Suppose A and B are two events that are not independent. Is the proba  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 42% (01:26) correct 58% (01:14) wrong based on 291 sessions

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Suppose A and B are two events that are not independent. Is the probability P(A and B) > 1/3?

(1) P(A) = 0.8 and P(B) = 0.7
(2) P(A or B) = 0.9

Kudos for a correct solution.

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Location: India
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GMAT Date: 05-10-2015
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Re: Suppose A and B are two events that are not independent. Is the proba  [#permalink]

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2
Answer should be A.
P(A U B) = P(A) + P(B) - P(A and B)

option A : P(A U B) = 0.8 + 0.7 - P(A and B) = 1.5 - P(A and B).
P(A U B) can not have value greater than 1, so, P(A and B) >= 0.5. Sufficient.
option B : Clearly Not Sufficient.
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Manager  Status: Gmat Prep
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Re: Suppose A and B are two events that are not independent. Is the proba  [#permalink]

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1
P(A or B)= P(A) + P(B) - P(A and B)

1) This gives an idea what is the least overlap is 1- .8 + 1- .3 =.5 which is greater than 1/3 hence this statement is sufficient.
2) P(A or B) does not tell us any thing about P(A) or P(B) insufficient.

Senior Manager  B
Joined: 28 Feb 2014
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Re: Suppose A and B are two events that are not independent. Is the proba  [#permalink]

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Bunuel wrote:
Suppose A and B are two events that are not independent. Is the probability P(A and B) > 1/3?

(1) P(A) = 0.8 and P(B) = 0.7
(2) P(A or B) = 0.9

Kudos for a correct solution.

Statement 1: We have individual probabilities for A and B, so we can obtain P(A) + P(B) - P(A and B)
Sufficient

Statement 2:
We need the individual probabilities
Insufficient

Math Expert V
Joined: 02 Sep 2009
Posts: 58445
Re: Suppose A and B are two events that are not independent. Is the proba  [#permalink]

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2
Bunuel wrote:
Suppose A and B are two events that are not independent. Is the probability P(A and B) > 1/3?

(1) P(A) = 0.8 and P(B) = 0.7
(2) P(A or B) = 0.9

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

Statement #1: this is very tricky. There is no cut-and-dry probability rule for this. we have to think about overlap. The total probability space, which encompasses anything that possibly could happen, has a size of 1, and P(A) and P(B) have to fit in this space. These two have a size of 0.8 and 0.7 respectively, so they are going to overlap. Think about it visually —
Attachment: gdspqop_img4.png [ 5.18 KiB | Viewed 7589 times ]

Push the P(A) = 0.8 all the way to the left (whatever that means!), leaving the 0.2 outside of A on the right. Now, push P(B) = 0.7 all the way to the right, leaving the 0.3 outside of B on the left. Suppose the 0.2 outside of A is inside B, and the 0.03 outside of B is inside A. This would be the minimum possible overlap, and even then the overlap, P(A and B), equals 0.5. Thus, P(A and B) ≥ 0.5, so it must be greater than 1/3. this statement allows us to give a definitive answer to the prompt question. This statement, alone and by itself, is sufficient.

Statement #2: forget everything we learned in the analysis of statement (1). Now, all we know is P(A or B) = 0.9, and we know absolutely nothing about P(A) or P(B). We can calculate nothing else. This statement, alone and by itself, is insufficient.

First sufficient, second not sufficient.

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Re: Suppose A and B are two events that are not independent. Is the proba  [#permalink]

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When the question says "not independent", what should I do?

Should I consider that the events are NOT mutually exclusive? Is it the same? Bc the answers here use the formula: P(A U B) = P(A) + P(B) - P(A and B)

Should I use the NOT independent events formula: P(AnB) = P(A).P(B|A)?

Thanks
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Re: Suppose A and B are two events that are not independent. Is the proba  [#permalink]

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guireif wrote:
When the question says "not independent", what should I do?

Should I consider that the events are NOT mutually exclusive? Is it the same? Bc the answers here use the formula: P(A U B) = P(A) + P(B) - P(A and B)

Should I use the NOT independent events formula: P(AnB) = P(A).P(B|A)?

Thanks

I have the same doubt.
Non-Human User Joined: 09 Sep 2013
Posts: 13275
Re: Suppose A and B are two events that are not independent. Is the proba  [#permalink]

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_________________ Re: Suppose A and B are two events that are not independent. Is the proba   [#permalink] 25 Nov 2018, 03:10
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