Last visit was: 05 Nov 2024, 11:43 It is currently 05 Nov 2024, 11:43
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

For a certain probability experiment the probability that

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

avatar
Hm3105
Intern
Intern
Joined: 17 Feb 2020
Posts: 16
Own Kudos [?]: 63 [9]
Given Kudos: 0
Send PM
For a certain probability experiment the probability that [#permalink] New post   10 Mar 2020, 11:05
1
8
Bookmarks
00:00

Question Stats:

26% (01:39) correct 73% (01:30) wrong based on 52 sessions

Hide Show timer Statistics

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
ShowHide Answer
Official Answer
C
Most Helpful Community Reply
User avatar
sujoykrdatta
GRE Instructor
Joined: 19 Jan 2020
Status:Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
Posts: 117
Own Kudos [?]: 265 [5]
Given Kudos: 0
GPA: 3.72
Send PM
Re: For a certain probability experiment the probability that [#permalink] New post   11 Mar 2020, 11:18
3
2
Bookmarks
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
General Discussion
avatar
Hm3105
Intern
Intern
Joined: 17 Feb 2020
Posts: 16
Own Kudos [?]: 63 [0]
Given Kudos: 0
Send PM
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
User avatar
sujoykrdatta
GRE Instructor
Joined: 19 Jan 2020
Status:Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
Posts: 117
Own Kudos [?]: 265 [3]
Given Kudos: 0
GPA: 3.72
Send PM
Re: For a certain probability experiment the probability that [#permalink] New post   11 Mar 2020, 12:57
3
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
avatar
Hm3105
Intern
Intern
Joined: 17 Feb 2020
Posts: 16
Own Kudos [?]: 63 [0]
Given Kudos: 0
Send PM
Re: For a certain probability experiment the probability that [#permalink] New post   11 Mar 2020, 23:19
Oh thank you¡ Got it now.
avatar
B
greenmonomer
Intern
Intern
Joined: 18 Jul 2021
Posts: 7
Own Kudos [?]: 0 [0]
Given Kudos: 15
Send PM
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.
avatar
B
greenmonomer
Intern
Intern
Joined: 18 Jul 2021
Posts: 7
Own Kudos [?]: 0 [0]
Given Kudos: 15
Send PM
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.
User avatar
sujoykrdatta
GRE Instructor
Joined: 19 Jan 2020
Status:Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
Posts: 117
Own Kudos [?]: 265 [2]
Given Kudos: 0
GPA: 3.72
Send PM
Re: For a certain probability experiment the probability that [#permalink] New post   12 Aug 2021, 03:15
2
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.

Posted from my mobile device
User avatar
sujoykrdatta
GRE Instructor
Joined: 19 Jan 2020
Status:Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
Posts: 117
Own Kudos [?]: 265 [1]
Given Kudos: 0
GPA: 3.72
Send PM
Re: For a certain probability experiment the probability that [#permalink] New post   12 Aug 2021, 03:18
1
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

Posted from my mobile device
avatar
B
greenmonomer
Intern
Intern
Joined: 18 Jul 2021
Posts: 7
Own Kudos [?]: 0 [0]
Given Kudos: 15
Send PM
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.
User avatar
G
motion2020
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Own Kudos [?]: 372 [1]
Given Kudos: 64
GRE 1: Q160 V152
Send PM
Re: For a certain probability experiment the probability that [#permalink] New post   13 Aug 2021, 06:48
1
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
User avatar
sujoykrdatta
GRE Instructor
Joined: 19 Jan 2020
Status:Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
Posts: 117
Own Kudos [?]: 265 [1]
Given Kudos: 0
GPA: 3.72
Send PM
Re: For a certain probability experiment the probability that [#permalink] New post   13 Aug 2021, 06:54
1
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
User avatar
G
motion2020
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Own Kudos [?]: 372 [1]
Given Kudos: 64
GRE 1: Q160 V152
Send PM
Re: For a certain probability experiment the probability that [#permalink] New post   13 Aug 2021, 07:00
1
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
User avatar
sujoykrdatta
GRE Instructor
Joined: 19 Jan 2020
Status:Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
Posts: 117
Own Kudos [?]: 265 [1]
Given Kudos: 0
GPA: 3.72
Send PM
Re: For a certain probability experiment the probability that [#permalink] New post   13 Aug 2021, 07:05
1
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.
User avatar
G
motion2020
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Own Kudos [?]: 372 [1]
Given Kudos: 64
GRE 1: Q160 V152
Send PM
For a certain probability experiment the probability that [#permalink] New post   13 Aug 2021, 07:22
1
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.
User avatar
bumpbot
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5006
Own Kudos [?]: 74 [0]
Given Kudos: 0
Send PM
Re: For a certain probability experiment the probability that [#permalink] New post   21 Aug 2022, 13:48
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Prep Club for GRE Bot
gmatclubot
Re: For a certain probability experiment the probability that [#permalink]
21 Aug 2022, 13:48
Moderators:
adewale223
GRE Instructor
77 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1111 posts
VibhuAnurag
GRE Instructor
228 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact