BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Probability DS

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 1169
Joined: Sun Jul 06, 2008 2:34 amFollowed by: 1 member
Thanked: 25 times
by aj5105 » Tue Jan 13, 2009 7:07 am
If the probability that event A will occur is 0.5, what is the probability that event B will occur?
(1) The probability that both A and B will occur is 0.3.
(2) The probability that at least one of the events will occur is 0.8.


P(A or B) = P(A) + P(B) - P(A and B)

1)P(A and B) = 0.3 --Not sufficient

2)P(A or B) = 0.8 --Not sufficient

1) + 2) Sufficient

Is my solution right? (especially St 2)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
Master | Next Rank: 500 Posts
Posts: 137
Joined: Thu Jan 08, 2009 1:27 am
Thanked: 7 times

by welcome » Tue Jan 13, 2009 7:25 am
IMO - B.

Here is the way I proceeded..

for using P(A or B) = P(A) + P(B) - P(A and B)
A) is NOT SUFF
b)
The probability that at least one of the events = 1 - Prob of no event (P(NO)).
0.8 = 1 - p(NO)
P(NO) = 0.2

P(NO) = 0.2 = (Prob of NOT A). (Probs of NOT B) = (1-0.5)(1-p(b))
=> 1-p(b) = 0.2/0.5 => p(b) = 3/5

Ans B.
Shubham.
590 >> 630 >> 640 >> 610 >> 600 >> 640 >> 590 >> 640 >> 590 >> 590
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 2134
Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members
Thanked: 237 times
GMAT Score:730

by logitech » Tue Jan 13, 2009 9:06 am
welcome wrote:IMO - B.

Here is the way I proceeded..

for using P(A or B) = P(A) + P(B) - P(A and B)
A) is NOT SUFF
b)
The probability that at least one of the events = 1 - Prob of no event (P(NO)).
0.8 = 1 - p(NO)
P(NO) = 0.2

P(NO) = 0.2 = (Prob of NOT A). (Probs of NOT B) = (1-0.5)(1-p(b))
=> 1-p(b) = 0.2/0.5 => p(b) = 3/5

Ans B.
Beautiful...
Attachments
hatsoff.jpg
LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 79
Joined: Wed Feb 06, 2008 7:52 am
Thanked: 2 times
GMAT Score:620

by yalanand » Tue Jan 13, 2009 12:00 pm
beautifully explained
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 45
Joined: Mon Dec 08, 2008 9:55 pm
Thanked: 4 times

by 720dreaming » Tue Jan 13, 2009 12:09 pm
How is A not sufficient?

(.5)(prob B)=(.3)

Prob B =60%

Am I missing something?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 2134
Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members
Thanked: 237 times
GMAT Score:730

by logitech » Tue Jan 13, 2009 4:18 pm
720dreaming wrote:How is A not sufficient?

(.5)(prob B)=(.3)

Prob B =60%

Am I missing something?
P(A or B) = P(A) + P(B) - P(A and B)
LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 45
Joined: Mon Dec 08, 2008 9:55 pm
Thanked: 4 times

by 720dreaming » Tue Jan 13, 2009 6:20 pm
Thanks Logitech. I am aware of the formula, but I am not sure if its relevent here.

A gives the prob of both events occuring. I would think that one EventA*EventB=prob of both events occuring.

For example, if the prob of event A is (.6) and prob of event B is (.2) is the prob of both events occuring not (.6)(.2)=(.48)?

It seems that we know the prob of both events occuring (.3) and the prob of event A occuring (.5), leaving event B to be (.6).

I've been looking over this question all day due to this issue, any comments would be appreciated!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 2134
Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members
Thanked: 237 times
GMAT Score:730

by logitech » Tue Jan 13, 2009 6:48 pm
720dreaming wrote:Thanks Logitech. I am aware of the formula, but I am not sure if its relevent here.

A gives the prob of both events occuring. I would think that one EventA*EventB=prob of both events occuring.

For example, if the prob of event A is (.6) and prob of event B is (.2) is the prob of both events occuring not (.6)(.2)=(.48)?

It seems that we know the prob of both events occuring (.3) and the prob of event A occuring (.5), leaving event B to be (.6).

I've been looking over this question all day due to this issue, any comments would be appreciated!
First of all,

I apologize for having you thinking on OUR careless mistake!

You are absolutely right.
These two types of probability are formulated as follows:
Probability of A and B
P(A and B) = P(A) × P(B).

In other words, the probability of A and B both occurring is the product of the probability of A and the probability of B.

Probability of A or B
P(A or B) = P(A) + P(B).

In other words, the probability of A or B occurring is the sum of the probability of A and the probability of B.
The question stem says AND so we need use the first equation: YOUR FORMULA

And yes your 0.6 is CORRECT and A is sufficient.

So is B :)

And the answer is D
LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 45
Joined: Mon Dec 08, 2008 9:55 pm
Thanked: 4 times

by 720dreaming » Tue Jan 13, 2009 7:01 pm
Not a problem, your other posts/solutions MORE THAN make up for it!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members
Location: Montreal
Thanked: 1090 times
GMAT Score:780

Re: Probability DS

by Ian Stewart » Wed Jan 14, 2009 12:53 am
aj5105 wrote:If the probability that event A will occur is 0.5, what is the probability that event B will occur?
(1) The probability that both A and B will occur is 0.3.
(2) The probability that at least one of the events will occur is 0.8.
This doesn't seem much like a real GMAT probability question, but since the question doesn't mention whether A and B are independent events, you have a lot less information here than you might think at first. The solution in the original post was correct; the others are not. In all of the solutions that followed the first, people have assumed that the events were *independent*. That is the only scenario when you can safely use the formula P(A AND B) = P(A)*P(B). If the events are not independent, that formula doesn't apply. It's easy to illustrate why neither statement is sufficient with a simple real world example:

Suppose you have ten cards, numbered from 1 to 10. You pick one card. Let A be "the number on the card is odd". Then the probability of A is 0.5.

If B is "the number on the card is less than 7", then there is a 0.3 chance that A and B both occur. If instead B is "the number on the card is less than 6", then there is also a 0.3 chance that A and B both occur. So 1) cannot be sufficient; the probability of B is 0.6 in the first case and 0.5 in the second case.

If B is "the number on the card is less than 7" then there is a 0.8 chance that A or B (or both) occurs. If B is "the number on the card is less than 8", there is again a 0.8 chance that A or B (or both) occurs. So 2) cannot be sufficient either.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1