Last visit was: 15 Sep 2026, 14:46 It is currently 15 Sep 2026, 14:46
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

The probability that event A occurs and event B does not occ

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 36148
Own Kudos [?]: 43314 [29]
Given Kudos: 27243
Send PM
The probability that event A occurs and event B does not occ [#permalink] New post   07 Aug 2020, 09:32
4
Expert Reply
25
Bookmarks
00:00

Question Stats:

47% (02:07) correct 52% (02:03) wrong based on 301 sessions

Hide Show timer Statistics

The probability that event A occurs and event B does not occur is greater than \(\frac{1}{4}\). The probability that event B occurs and event A does not occur is greater than \(\frac{1}{4}\) . The probability that neither of the events A and B occurs is greater than \(\frac{1}{8}\).


Quantity A
Quantity B
The probability that both of the events A and B occur
\( \frac{1}{4}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given

Kudos for the right solution and explanation
ShowHide Answer
Official Answer
D
Most Helpful Community Reply
avatar
chacinluis
Manager
Manager
Joined: 22 Jan 2020
Posts: 120
Own Kudos [?]: 261 [9]
Given Kudos: 10
Send PM
Re: The probability that event A occurs and event B does not occ [#permalink] New post   08 Aug 2020, 08:41
3
6
Bookmarks
Attachment:
vennDiagram.PNG
vennDiagram.PNG [ 8.33 KiB | Viewed 17645 times ]
We have Events A and B, and sample space S

P(A,B complement)>.25
P(A complement, B)>.25
P(A complement, B complement)> .125

We are comparing P(A, B) with 0.25


Look at the Venn diagram posted
First we notice that P(A,B complement)+ P(A complement, B)+ P(A complement, B complement)+ P(A,B)= P(S)= 1

Then we ask ourselves: when will P(A, B) be at its max?
When P(A,B complement), P(A complement, B), and P(A complement, B complement) are its lowest values.

That is when
P(A,B complement)=.25
P(A complement, B)= .25
P(A complement, B complement)= .125

Therefore
P(A,B)<1-P(A,B complement)- P(A complement, B)- P(A complement, B complement)= 1 - .25 - .25 - .125= .375

Therefore P(A,B) could be more or less than .25

Final Answer: D
General Discussion
User avatar
Farina
Senior Manager
Senior Manager
Joined: 10 Feb 2020
Posts: 496
Own Kudos [?]: 378 [0]
Given Kudos: 299
Send PM
Re: The probability that event A occurs and event B does not occ [#permalink] New post   08 Aug 2020, 06:03
Explanation plz?
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 36148
Own Kudos [?]: 43314 [0]
Given Kudos: 27243
Send PM
Re: The probability that event A occurs and event B does not occ [#permalink] New post   08 Aug 2020, 10:31
Expert Reply
Thank you Sir.

I admire your explanation
avatar
rydercourtney1
Intern
Intern
Joined: 10 Sep 2020
Posts: 26
Own Kudos [?]: 13 [0]
Given Kudos: 0
Send PM
Re: The probability that event A occurs and event B does not occ [#permalink] New post   10 Sep 2020, 12:03
can someone list an actual #, ie .4 or 3/10 for A and for B that will satisfy the original premise?
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12827 [5]
Given Kudos: 136
Send PM

Top Member of the Month
Re: The probability that event A occurs and event B does not occ [#permalink] New post   11 Sep 2020, 05:37
3
2
Bookmarks
Carcass wrote:
The probability that event A occurs and event B does not occur is greater than \(\frac{1}{4}\). The probability that event B occurs and event A does not occur is greater than \(\frac{1}{4}\) . The probability that neither of the events A and B occurs is greater than \(\frac{1}{8}\).


Quantity A
Quantity B
The probability that both of the events A and B occur
\( \frac{1}{4}\)


We can use a Double Matrix to show all of the probabilities (for more on this watch the video below)

So, one possible case that meets all of the conditions is as follows:
Image
In this case we get:
Quantity A: 0.35
Quantity B: 1/4
Quantity A is greater


Another possible case is as follows:
Image
In this case we get:
Quantity A: 0.22
Quantity B: 1/4
Quantity B is greater


Answer: D

Cheers,
Brent

Double Matrix Method
avatar
rydercourtney1
Intern
Intern
Joined: 10 Sep 2020
Posts: 26
Own Kudos [?]: 13 [0]
Given Kudos: 0
Send PM
Re: The probability that event A occurs and event B does not occ [#permalink] New post   13 Sep 2020, 05:05
Thank you for your great effort! Maybe I am reading the question wrong. But A occurs and B does not occur would be .35 multiplied by .13 which is not greater than 1/4. Also, do the probabilities of occurring and not occurring have to add up to 1?
avatar
B
KC15
Intern
Intern
Joined: 08 Aug 2022
Posts: 49
Own Kudos [?]: 46 [0]
Given Kudos: 98
Send PM
Re: The probability that event A occurs and event B does not occ [#permalink] New post   28 Aug 2022, 13:04
P(A, not B) > 1/4
P(not A, B) > 1/4
P(not A, not B) > 1/8
P(A, B) < 1-1/4-1/4-1/8 --> 8/8 - 2/8 - 2/8 - 1/8 --> 3/8

P(A,B)<3/8
so P(A,B) could be greater or less than 1/4=2/8
for example, 2.5/8 (greater than 1/4=2/8) or 1/8 (less than 1/4 = 2/8)
so the answer is D
User avatar
S
adewale223
GRE Instructor
Joined: 06 Nov 2023
Posts: 166
Own Kudos [?]: 181 [2]
Given Kudos: 47
Send PM
The probability that event A occurs and event B does not occ [#permalink] New post   06 Jan 2024, 08:51
2
A x B' > 1/4...........i


B x A' > 1/4.........ii

A' x B' > 1/8.........iii



From equation i


B' > 1/4A


From equation ii

A' > 1/4B


sub in equation iii



1/4B x 1/4A > 1/8


Reciprocal reverses inequality sign


16AB < 8

AB < 1/2


Some values will be greater than 1/4 but as you consider other values A becomes less than B

Answer is D.

Adewale Fasipe, GRE, GMAT quant instructor from Nigeria
https://www.teacheron.com/tutor-profile/8tG7?r=8tG7
avatar
B
someone99
Intern
Intern
Joined: 20 Jun 2024
Posts: 8
Own Kudos [?]: 4 [0]
Given Kudos: 15
Send PM
Re: The probability that event A occurs and event B does not occ [#permalink] New post   13 Jan 2025, 04:12
adewale223 wrote:
A x B' > 1/4...........i


B x A' > 1/4.........ii

A' x B' > 1/8.........iii



From equation i


B' > 1/4A


From equation ii

A' > 1/4B


sub in equation iii



1/4B x 1/4A > 1/8


Reciprocal reverses inequality sign


16AB < 8

AB < 1/2


Some values will be greater than 1/4 but as you consider other values A becomes less than B

Answer is D.

Adewale Fasipe, GRE, GMAT quant instructor from Nigeria


The problem doesnt state that A and B are independent, so i dont think P(A , B) = P( A) * P(B)
User avatar
G
tyrant100
GRE Forum Moderator
Joined: 08 Sep 2024
Posts: 144
Own Kudos [?]: 91 [0]
Given Kudos: 268
Send PM
The probability that event A occurs and event B does not occ [#permalink] New post   31 Jan 2026, 06:24
Im gonna use some obnoxious method for this
Brace yourself

P(A occurs but not B) = 0.25 + x

Cuz it says greater than 0.25

Same for
P(B occurs but not A) = 0.25 + y

and also for

P(Neither B or A occurs) = 0.125 + z

Now yk this

Total = quantity 1 + quantity 2 - both + neither

1 = 0.25+(common part) + x + 0.25 + y + (common part) - (common part) + 0.125 + 7

0.375 = x + y + z + common part

Now common part is your quantity A

0.375 - (x+y+z) = common part

Now you can rewrite it as

0.125 + 0.25 - (x+y+z) = common part

Cancel out 0.25 from both quantity A and B

You'll get quantity A as
0.125-(x+y+z)

And quantity B as 0

Now

x+y+z can be 0.125 or some positive quantity less than 0.125

So its D

kudos is appreciated
avatar
B
nickthome
Intern
Intern
Joined: 15 Jan 2026
Posts: 10
Own Kudos [?]: 5 [0]
Given Kudos: 0
Send PM
Re: The probability that event A occurs and event B does not occ [#permalink] New post   15 Feb 2026, 16:51
A fairly simplistic numerical evaluation:

We know P(A, no B) > 1/4, P(B, no A) > 1/4, P(no A, no B) > 1/8.

We can check some values, starting with 16 in the denominator to find the sensitivity threshold:

Case 1 (16 in denom):
P(A, no B) = 5/16 (slightly greater than 1/4)
P(B, no A) = 5/16 (slightly greater than 1/4)
P(no A, no B) = 3/16 (slightly greater than 1/8)
(5 + 5 + 3)/16 = 13/16, remainder of 3/16 < 1/4

Case 2 (64 in denom):
P(A, no B) = 17/64 (slightly greater than 1/4)
P(B, no A) = 17/64 (slightly greater than 1/4)
P(no A, no B) = 9/64 (slightly greater than 1/8)
(17 + 17 + 9)/64 = 43/64, remainder of 21/64 > 1/4

Therefore, with contradicting values as the denominator increase, we have the answer of D
Prep Club for GRE Bot
gmatclubot
Re: The probability that event A occurs and event B does not occ [#permalink]
15 Feb 2026, 16:51
Moderators:
adewale223
GRE Instructor
166 posts
bronaugust
GRE Forum Moderator
37 posts
VibhuAnurag
GRE Instructor
275 posts
Nsp10
Moderator
45 posts
tyrant100
GRE Forum Moderator
144 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 | Advertise