NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 03:31 It is currently 25 Apr 2024, 03:31
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

The probability that an event A occurs is 1/2 and the probability that

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10161
Own Kudos [?]: 16594 [4]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
The probability that an event A occurs is 1/2 and the probability that [#permalink] New post   09 Nov 2017, 00:38
1
Kudos
3
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

80% (00:38) correct 20% (00:50) wrong based on 134 sessions
Hide Show timer Statistics
[GMAT math practice question]

The probability that an event A occurs is 1/2 and the probability that an even B occurs is 1/3. If event A and event B are independent, what is the probability that event A occurs but event B does not occur?

A. 1/6
B. 1/3
C. 1/2
D. 2/3
E. 5/6
ShowHide Answer
Official Answer
B
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10161
Own Kudos [?]: 16594 [2]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: The probability that an event A occurs is 1/2 and the probability that [#permalink] New post   09 Nov 2017, 01:00
1
Kudos
1
Bookmarks
Expert Reply
=>

Since events A and B are independent, P(A∩B) = P(A) ∙P(B).
The probability P(A-B) = P(A) - P(A∩B) = P(A) - P(A) ∙P(B) = 1/2 – (1/2)(1/3) = 1/2 – 1/6 = 2/6 = 1/3.

Thus, the answer is B.
Answer: B
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3043
Own Kudos [?]: 6272 [2]
Given Kudos: 1646
Send PM
Re: The probability that an event A occurs is 1/2 and the probability that [#permalink] New post   12 Nov 2017, 08:47
2
Kudos
Expert Reply
MathRevolution wrote:

The probability that an event A occurs is 1/2 and the probability that an even B occurs is 1/3. If event A and event B are independent, what is the probability that event A occurs but event B does not occur?

A. 1/6
B. 1/3
C. 1/2
D. 2/3
E. 5/6


The probability that event B does not occur is 1 - 1/3 = 2/3.

Since we want the probability that A occurs AND that B does not occur, we multiply their respective probabilities. Thus, the probability that event A occurs but event B does not occur is 1/2 x 2/3 = 1/3.

Answer: B
User avatar
B
Vorovski
Intern
Intern
Joined: 16 Oct 2017
Posts: 25
Own Kudos [?]: 27 [0]
Given Kudos: 79
Location: Ireland
Concentration: Healthcare, Finance
Send PM
Re: The probability that an event A occurs is 1/2 and the probability that [#permalink] New post   21 Dec 2017, 02:34
MathRevolution wrote:
=>

Since events A and B are independent, P(A∩B) = P(A) ∙P(B).
The probability P(A-B) = P(A) - P(A∩B) = P(A) - P(A) ∙P(B) = 1/2 – (1/2)(1/3) = 1/2 – 1/6 = 2/6 = 1/3.

Thus, the answer is B.
Answer: B



Dear instructor, could you be so kind to explain that \(P(A-B) = P(A) - P(A∩B)\) actually means. I know that in a Venn diagram \(A∩B\) means itersection but I can't figure out how it works for our problem. Thanks
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32665
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: The probability that an event A occurs is 1/2 and the probability that [#permalink] New post   20 Sep 2023, 19:32
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
gmatclubot
Re: The probability that an event A occurs is 1/2 and the probability that [#permalink]
20 Sep 2023, 19:32
Moderators:
Bunuel
Math Expert
92912 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions