It is currently 10 Aug 2020, 10:02
My Tests

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.

The events A and B are independent, the probability that

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
Joined: 13 May 2019
Posts: 10
Followers: 0

Kudos [?]: 0 [0], given: 12

The events A and B are independent, the probability that [#permalink] New post 24 Mar 2020, 08:58
00:00

Question Stats:

58% (01:47) correct 41% (03:27) wrong based on 12 sessions
The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 8 times the probability that both events A and B occur. What is the probability that event A occurs?

A. 1/12
B. 1/8
C. 1/6
D. 1/3
E. 2/3
[Reveal] Spoiler: OA
1 KUDOS received
Founder
Founder
User avatar
Joined: 18 Apr 2015
Posts: 12532
Followers: 267

Kudos [?]: 3163 [1] , given: 11602

CAT Tests
Re: The events A and B are independent, the probability that [#permalink] New post 24 Mar 2020, 09:39
1
This post received
KUDOS
Expert's post
a = 2b

Probability (either A or B or both) = 8 times Probability (A and B)
a*(1-b) + b*(1-a) + ab = 8*ab

Substituting a=2b in the second equation:

2b*(1-b) + b*(1-2b) + 2b*b = 8*2b*b

3b-2b^2 = 16b^2
3b = 18b^2
b = 3/18 = 1/6

So, a = 2b = 1/3
_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

1 KUDOS received
Intern
Intern
Joined: 14 May 2019
Posts: 29
Followers: 0

Kudos [?]: 27 [1] , given: 3

Re: The events A and B are independent, the probability that [#permalink] New post 25 Mar 2020, 05:44
1
This post received
KUDOS
P(A or B) = P(A) + P(B) - P(A and B).....(1)
since A and B are independent, then P(A and B)= P(A) * P(B)
Given,
P(A or B) = 8*P(A and B)
P(A) = 2*P(B) ; P(B) = P(A)/2
therefore,
8* P(A and B) = 8 (P(A) *P(A)/2) = 4 (P(A)^2)
substituting the given values into (1),
4(P(A)^2) = P(A) + P(A)/2 -P(A)^2)/2
4(P(A)^2) + P(A)^2/2 =3P(A)/2
9(P(A)^2)/2 = 3P(A)/2
Hence,
P(A) =1/3
Re: The events A and B are independent, the probability that   [#permalink] 25 Mar 2020, 05:44
Display posts from previous: Sort by

The events A and B are independent, the probability that

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.