GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Oct 2019, 17:46

Close

GMAT 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 GMAT 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.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

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

Show Tags

New post 06 Mar 2015, 07:25
3
16
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

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

HideShow timer Statistics

Most Helpful Community Reply
Manager
Manager
avatar
Joined: 25 Mar 2014
Posts: 128
Location: India
Concentration: Operations, Finance
GMAT Date: 05-10-2015
GPA: 3.51
WE: Programming (Computer Software)
Re: Suppose A and B are two events that are not independent. Is the proba  [#permalink]

Show Tags

New post 06 Mar 2015, 22:56
6
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.
_________________
Please give Kudos to the post if you liked.
General Discussion
Manager
Manager
User avatar
Status: Gmat Prep
Joined: 22 Jul 2011
Posts: 73
GMAT ToolKit User
Re: Suppose A and B are two events that are not independent. Is the proba  [#permalink]

Show Tags

New post 06 Mar 2015, 08:57
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.

answer is A
Senior Manager
Senior Manager
User avatar
B
Joined: 28 Feb 2014
Posts: 291
Location: United States
Concentration: Strategy, General Management
Reviews Badge
Re: Suppose A and B are two events that are not independent. Is the proba  [#permalink]

Show Tags

New post 07 Mar 2015, 15:05
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
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58445
Re: Suppose A and B are two events that are not independent. Is the proba  [#permalink]

Show Tags

New post 08 Mar 2015, 16:14
2
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
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.

Answer = A.
_________________
Intern
Intern
User avatar
B
Joined: 05 Jul 2016
Posts: 16
Location: Brazil
Concentration: Finance, Entrepreneurship
WE: Analyst (Investment Banking)
Re: Suppose A and B are two events that are not independent. Is the proba  [#permalink]

Show Tags

New post 18 Sep 2017, 16:22
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
Intern
Intern
User avatar
B
Joined: 18 Apr 2017
Posts: 15
Location: Brazil
WE: Corporate Finance (Energy and Utilities)
Re: Suppose A and B are two events that are not independent. Is the proba  [#permalink]

Show Tags

New post 28 Oct 2017, 10:59
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.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13275
Re: Suppose A and B are two events that are not independent. Is the proba  [#permalink]

Show Tags

New post 25 Nov 2018, 03:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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.
_________________
GMAT Club Bot
Re: Suppose A and B are two events that are not independent. Is the proba   [#permalink] 25 Nov 2018, 03:10
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





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