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Suppose A and B are two events that are not independent. Is the proba

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

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

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New post 06 Mar 2015, 21:56
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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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Re: Suppose A and B are two events that are not independent. Is the proba  [#permalink]

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New post 06 Mar 2015, 07:57
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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.

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

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New post 07 Mar 2015, 14:05
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

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

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New post 08 Mar 2015, 15:14
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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.


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
gdspqop_img4.png [ 5.18 KiB | Viewed 6106 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.

Answer = A.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 18 Sep 2017, 15:22
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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New post 28 Oct 2017, 09:59
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.
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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 &nbs [#permalink] 25 Nov 2018, 02:10
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