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For a certain probability experiment the probability that

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Hm3105
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For a certain probability experiment the probability that [#permalink] New post   10 Mar 2020, 11:05
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For a certain probability experiment the probability that event A will occur is 3/4 and the probability that event B will occur is 1/2 . Which of the following values could be the probability that event A ∩ B will occur.

A)1/6
B)1/5
C)1/3
D)2/3
E)3/4
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C
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Re: For a certain probability experiment the probability that [#permalink] New post   11 Mar 2020, 11:18
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Hm3105 wrote:
For a certain probability experiment the probability that event A will occur is 3/4 and the probability that event B will occur is 1/2 . Which of the following values could be the probability that event A ∩ B will occur.

A)1/6
B)1/5
C)1/3
D)2/3
E)3/4



Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B

=> Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B

=> Probability of A U B = 3/4 + 1/2 - Probability of A ∩ B

=> Probability of A U B = 5/4 - Probability of A ∩ B

The maximum value of Probability of A U B is 1

=> Probability of A ∩ B = 5/4 - 1 = 1/4 or higher

=> Minimum value of Probability of A ∩ B = 1/4

However, the maximum value of Probability of A ∩ B will be the smaller of the individual probabilities of A and B = 1/2

The only value between (inclusive) 1/4 and 1/2 is 1/3

Answer C
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Re: For a certain probability experiment the probability that [#permalink] New post   11 Mar 2020, 12:04
sujoykrdatta wrote:
Hm3105 wrote:
For a certain probability experiment the probability that event A will occur is 3/4 and the probability that event B will occur is 1/2 . Which of the following values could be the probability that event A ∩ B will occur.

A)1/6
B)1/5
C)1/3
D)2/3
E)3/4



Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B

=> Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B

=> Probability of A U B = 3/4 + 1/2 - Probability of A ∩ B

=> Probability of A U B = 5/4 - Probability of A ∩ B

The maximum value of Probability of A U B is 1

=> Probability of A ∩ B = 5/4 - 1 = 1/4 or higher

=> Minimum value of Probability of A ∩ B = 1/4

However, the maximum value of Probability of A ∩ B will be the smaller of the individual probabilities of A and B = 1/2

The only value between (inclusive) 1/4 and 1/2 is 1/3

Answer C


Shouldn't the max value of A∩B be the bigger of the two individual probability? Please explain this part
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Re: For a certain probability experiment the probability that [#permalink] New post   11 Mar 2020, 12:57
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Hm3105 wrote:
sujoykrdatta wrote:
Hm3105 wrote:
For a certain probability experiment the probability that event A will occur is 3/4 and the probability that event B will occur is 1/2 . Which of the following values could be the probability that event A ∩ B will occur.

A)1/6
B)1/5
C)1/3
D)2/3
E)3/4



Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B

=> Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B

=> Probability of A U B = 3/4 + 1/2 - Probability of A ∩ B

=> Probability of A U B = 5/4 - Probability of A ∩ B

The maximum value of Probability of A U B is 1

=> Probability of A ∩ B = 5/4 - 1 = 1/4 or higher

=> Minimum value of Probability of A ∩ B = 1/4

However, the maximum value of Probability of A ∩ B will be the smaller of the individual probabilities of A and B = 1/2

The only value between (inclusive) 1/4 and 1/2 is 1/3

Answer C


Shouldn't the max value of A∩B be the bigger of the two individual probability? Please explain this part



When 2 sets A and B intersect each other, the maximum value of the intersection is the minimum of the two sets

Observe that the intersection is the part that can go common, so cannot be the larger of the 2 sets

Say: A = set of 10 students who like coffee and B = set of 20 students who like tea => the intersection can at the most be 10 students

Similar is the case of probability as well
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Re: For a certain probability experiment the probability that [#permalink] New post   11 Mar 2020, 23:19
Oh thank you¡ Got it now.
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Re: For a certain probability experiment the probability that [#permalink] New post   12 Aug 2021, 02:36
sujoykrdatta
Why did not you consider mutually exclusive case? as I can think, two scenarios should be counted, mutually exclusive and inclusive.

attention Carcass
thanks in advance.
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Re: For a certain probability experiment the probability that [#permalink] New post   12 Aug 2021, 03:07
For a certain probability experiment, the probability that event F will occur is 1/4 and the probability that even G will occur is 3/5. Which of the following values could be the probability that the event F∩G (both) will occur?
A) 1/5
B) 1/4
C) 3/5
D) 17/20

answer a and b... as max to min limit is 0 to 1/4...
i think these two q are same ... then why the limit is 1/4 to 1/2 here.
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Re: For a certain probability experiment the probability that [#permalink] New post   12 Aug 2021, 03:15
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greenmonomer wrote:
sujoykrdatta
Why did not you consider mutually exclusive case? as I can think, two scenarios should be counted, mutually exclusive and inclusive.

attention Carcass
thanks in advance.


Sum of probabilities of A and B exceeds 1. They cannot be mutually exclusive.

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Re: For a certain probability experiment the probability that [#permalink] New post   12 Aug 2021, 03:18
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greenmonomer wrote:
For a certain probability experiment, the probability that event F will occur is 1/4 and the probability that even G will occur is 3/5. Which of the following values could be the probability that the event F∩G (both) will occur?
A) 1/5
B) 1/4
C) 3/5
D) 17/20

answer a and b... as max to min limit is 0 to 1/4...
i think these two q are same ... then why the limit is 1/4 to 1/2 here.



The questions APPEAR to be the same
Here the values can be mutually exclusive since their sum is less than 1

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Re: For a certain probability experiment the probability that [#permalink] New post   12 Aug 2021, 07:27
sujoykrdatta

Thank you so much ... I have noticed that too ... but I was not confident enough about that logic.
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Re: For a certain probability experiment the probability that [#permalink] New post   13 Aug 2021, 06:48
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I believe the issue is technically related to the notation included with the first reply

Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B

I would say if we consider P(A) as mutually exclusive, and this is possible, then P(A only)=P(A)-P(A ∩ B).
The same is needed for P(B) to be mutually exclusive, and P(B only)=P(B)-P(A ∩ B)

Then, we can combine (sum) all probabilities: P(A only)+P(B only)+P(A ∩ B), which is the same as P(A)-P(A ∩ B) + P(B)-P(A ∩ B) + P(A ∩ B) = Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B
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Re: For a certain probability experiment the probability that [#permalink] New post   13 Aug 2021, 06:54
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motion2020 wrote:
I believe the issue is technically related to the notation included with the first reply

Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B

I would say if we consider P(A) as mutually exclusive, and this is possible, then P(A only)=P(A)-P(A ∩ B).
The same is needed for P(B) to be mutually exclusive, and P(B only)=P(B)-P(A ∩ B)

Then, we can combine (sum) all probabilities: P(A only)+P(B only)+P(A ∩ B), which is the same as P(A)-P(A ∩ B) + P(B)-P(A ∩ B) + P(A ∩ B) = Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B



Quoting "I would say if we consider P(A) as mutually exclusive"
Mutually means there has to be someone else...
Who is A mutually exclusive to? To B? Then A and B cannot have any intersection. Their intersection is 0. That's what mutually exclusive means.

A and B cannot be mutually exclusive here since they add up to more than 1

Posted from my mobile device
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Re: For a certain probability experiment the probability that [#permalink] New post   13 Aug 2021, 07:00
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A is an event. B is an event too.
Probabilities defined for P(A) or P(A only) are different. I am appealing to sample size (borel algebra) for any probability and set theory, etc.
sujoykrdatta wrote:
motion2020 wrote:
I believe the issue is technically related to the notation included with the first reply

Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B

I would say if we consider P(A) as mutually exclusive, and this is possible, then P(A only)=P(A)-P(A ∩ B).
The same is needed for P(B) to be mutually exclusive, and P(B only)=P(B)-P(A ∩ B)

Then, we can combine (sum) all probabilities: P(A only)+P(B only)+P(A ∩ B), which is the same as P(A)-P(A ∩ B) + P(B)-P(A ∩ B) + P(A ∩ B) = Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B



Quoting "I would say if we consider P(A) as mutually exclusive"
Mutually means there has to be someone else...
Who is A mutually exclusive to? To B? Then A and B cannot have any intersection. Their intersection is 0. That's what mutually exclusive means.

A and B cannot be mutually exclusive here since they add up to more than 1

Posted from my mobile device
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Re: For a certain probability experiment the probability that [#permalink] New post   13 Aug 2021, 07:05
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motion2020 wrote:
A is an event. B is an event too.
Probabilities defined for P(A) or P(A only) are different. I am appealing to sample size (borel algebra) for any probability and set theory, etc.
sujoykrdatta wrote:
motion2020 wrote:
I believe the issue is technically related to the notation included with the first reply

Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B

I would say if we consider P(A) as mutually exclusive, and this is possible, then P(A only)=P(A)-P(A ∩ B).
The same is needed for P(B) to be mutually exclusive, and P(B only)=P(B)-P(A ∩ B)

Then, we can combine (sum) all probabilities: P(A only)+P(B only)+P(A ∩ B), which is the same as P(A)-P(A ∩ B) + P(B)-P(A ∩ B) + P(A ∩ B) = Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B



Quoting "I would say if we consider P(A) as mutually exclusive"
Mutually means there has to be someone else...
Who is A mutually exclusive to? To B? Then A and B cannot have any intersection. Their intersection is 0. That's what mutually exclusive means.

A and B cannot be mutually exclusive here since they add up to more than 1

Posted from my mobile device



Note: Probabilities defined for P(A) or P(A only) are different.

Yes, exactly.
That however has nothing to do with A and B being exclusive. A and B here cannot ve exclusive. I already told you what exclusive refers to. Please check that.
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For a certain probability experiment the probability that [#permalink] New post   13 Aug 2021, 07:22
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IMO, my post is for learning purpose, but never arguing

"I would say if we consider P(A) as mutually exclusive, and this is possible, then P(A only)=P(A)-P(A ∩ B)"
Event A contains a subset, which has its defined probability P(A only); it's considered as being mutually exclusive with other samples. Event A and its probability of P(A) entirely, of course, cannot be considered as mutually exclusive to event B.
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Re: For a certain probability experiment the probability that [#permalink] New post   21 Aug 2022, 13:48
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Re: For a certain probability experiment the probability that [#permalink]
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