GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 02 Jun 2020, 00:16

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

The events A and B are independent. The probability that event A occu

  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: 64130
The events A and B are independent. The probability that event A occu  [#permalink]

Show Tags

New post 11 Sep 2015, 00:59
3
23
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

55% (02:12) correct 45% (01:35) wrong based on 221 sessions

HideShow timer Statistics

Most Helpful Community Reply
Manager
Manager
avatar
Joined: 17 Aug 2015
Posts: 95
Location: India
Concentration: Strategy, General Management
Schools: Duke '19 (II)
GMAT 1: 750 Q49 V42
GPA: 4
WE: Information Technology (Investment Banking)
GMAT ToolKit User
Re: The events A and B are independent. The probability that event A occu  [#permalink]

Show Tags

New post 11 Sep 2015, 01:55
5
P(A U B) = P(A) + P(B) - P(A intersection B)

for independent events, the probability of both occuring

P(A intersection B) = P(A) * P(B)

So, 0.94 = 0.6 + P(B) - P(B) * 0.6

So, P(B) = 0.85

Answer: (E)
General Discussion
Intern
Intern
avatar
Joined: 02 Sep 2015
Posts: 4
Re: The events A and B are independent. The probability that event A occu  [#permalink]

Show Tags

New post 11 Sep 2015, 01:47
3
1
At least one of the events A or B occurs means
1) Event A occur (Ao)and Event B does not (Bd)
2) Event B occur (Bo) and Event A does not (Ad)
3) Both events A and B occur (Ao & Bo)

Hence 0.94 = Ao*Bd + Bo*Ad + Ao*Bo

Does not occur is equal to one minus the probability it occurs

WKT The probability that event A occurs is 0.6 ie Ao = 0.6

0.94= 0.6*(1-Bo)+ Bo*(1-Ao) + Ao*Bo
0.94=0.6*(1-Bo) + Bo*(1-0.6)+ 0.6*Bo
On simplification we get,
The probability that event B occurs (Bo) = 0.85
Manager
Manager
avatar
S
Joined: 13 Mar 2013
Posts: 153
Location: United States
Concentration: Leadership, Technology
GPA: 3.5
WE: Engineering (Telecommunications)
Re: The events A and B are independent. The probability that event A occu  [#permalink]

Show Tags

New post 11 Sep 2015, 12:32
2
The events A and B are independent. The probability that event A occurs is 0.6, and the probability that at least one of the events A or B occurs is 0.94. What is the probability that event B occurs?

(A) 0.34
(B) 0.65
(C) 0.72
(D) 0.76
(E) 0.85

As given independent event p( A and B) = pA *pB
p(AorB) = 0.94


p(AorB) = pA + pB - p( A and B)
= pA + pB - pA *pB
0.94 =0.6 + pB - (0.6*pB)

On solving the above we get
pB = 0.85
E ans .
_________________
Regards ,
Manager
Manager
User avatar
Joined: 10 May 2014
Posts: 134
The events A and B are independent. The probability that event A occu  [#permalink]

Show Tags

New post 12 Sep 2015, 13:48
1
Probability of A
- Yes: 0.6
- No: 0.4

Probability of B
- Yes: Y
- No: N

Probability of at least A or B = 1 - (0.4)(N)
0.94 = 1 - (0.4)N
N = 0.15

1 - N = Y
1 - 0.15 = Y
Y = 0.85

Answer Choice E
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64130
Re: The events A and B are independent. The probability that event A occu  [#permalink]

Show Tags

New post 14 Sep 2015, 05:03
1
1
Bunuel wrote:
The events A and B are independent. The probability that event A occurs is 0.6, and the probability that at least one of the events A or B occurs is 0.94. What is the probability that event B occurs?

(A) 0.34
(B) 0.65
(C) 0.72
(D) 0.76
(E) 0.85

Kudos for a correct solution.


KAPLAN OFFICIAL SOLUTION:

In order to find the probability that event B occurs in this problem, we need to set up an equation that includes the probabilities we are given and which allows us to solve for B. We are told that the probability that at least one of A or B occurring is 0.94. ‘At least one of A or B’ means that an outcome is desired if A occurs and B does not, B occurs and A does not or A and B both occur.

It is important to remember two rules of probability here. First, when you encounter an ‘or’ situation you add and when you see an ‘and’ situation you multiply. Second, the probability that an event does NOT occur is equal to one minus the probability it does occur.

Based on these rules, we can translate ‘at least one of A or B occurs is 0.94’ to the following equation:

.6B [the probability that both A and B occur] + .6(1-B) [the probability that A occurs and B does not] + B(1-.6) [the probability that B occurs and A does not] = .94

We can simplify this equation to .6B + .6(1-B) + .4B = .94 and solve for B.

.6B + .6(1-B) + .4B = .94

.6B + .6 – .6B + .4B = .94

.6 + .4B = .94

.4B = .34

B = .34/.4

B = 34/40 = .85

Thus, our answer is 0.85, or answer choice (E).
_________________
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2432
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Reviews Badge
Re: The events A and B are independent. The probability that event A occu  [#permalink]

Show Tags

New post 27 Mar 2016, 19:39
1
Bunuel wrote:
The events A and B are independent. The probability that event A occurs is 0.6, and the probability that at least one of the events A or B occurs is 0.94. What is the probability that event B occurs?

(A) 0.34
(B) 0.65
(C) 0.72
(D) 0.76
(E) 0.85

Kudos for a correct solution.



very very tricky one indeed.
P(A)=0.6
P(A or B) = 0.94
since both are independent, P(A and B) is P(A)*P(B)
using OR formula we get:
P(A or B) = P(A) + P(B) - P(A and B)
0.94 = 0.6 + P(B) - P(B)*0.6
0.34 = P(B) - 0.6*P(B)
factor P(B)
0.34 = P(B)(1-0.6)
0.34 = P(B)*(0.4)
PB = 0.34/0.4
use fractions better
34/40 -> 17/20 - multiply by 5 -> 85/100 so 0.85 - E
Manager
Manager
User avatar
S
Joined: 28 Nov 2017
Posts: 135
Location: Uzbekistan
Re: The events A and B are independent. The probability that event A occu  [#permalink]

Show Tags

New post 11 Apr 2018, 03:53
Bunuel wrote:
The events A and B are independent. The probability that event A occurs is 0.6, and the probability that at least one of the events A or B occurs is 0.94. What is the probability that event B occurs?

(A) 0.34
(B) 0.65
(C) 0.72
(D) 0.76
(E) 0.85

Kudos for a correct solution.


Hi!
I have an alternative solution.

Prob A won't occur =1-0.6=0.4
Let's assume that Prob B won't occur x.

Then, Prob both A and B together will not occur is 0.4x=1-0.94=0.06
So, x=0.15

Thus, Prob B will occur is 1-0.15=0.85

Hence, E.
_________________
Kindest Regards!
Tulkin.
Manager
Manager
avatar
B
Joined: 05 Oct 2019
Posts: 53
Location: Georgia
Concentration: Marketing, General Management
GMAT 1: 540 Q37 V27
GPA: 2.88
Re: The events A and B are independent. The probability that event A occu  [#permalink]

Show Tags

New post 22 Jan 2020, 07:43
P(at least one of them) = P(A) + P(B) - P(A x B)
0.94 = 0.6 + B - 0.6xB
0.94 = 0.6 + 0.4B
0.34 = 0.4B
B = 0.34/0.4 (same as 17/20) = 0.85 E.
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10640
Location: United States (CA)
Re: The events A and B are independent. The probability that event A occu  [#permalink]

Show Tags

New post 24 Jan 2020, 09:23
Bunuel wrote:
The events A and B are independent. The probability that event A occurs is 0.6, and the probability that at least one of the events A or B occurs is 0.94. What is the probability that event B occurs?

(A) 0.34
(B) 0.65
(C) 0.72
(D) 0.76
(E) 0.85

Kudos for a correct solution.


We can use the formula:

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

Since A and B are independent, P(A and B) = P(A) * P(B). Therefore, we have:

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

0.94 = 0.6 + P(B) - 0.6 * P(B)

0.34 = 0.4 * P(B)

P(B) = 0.34/0.4 = 0.85

Answer: E


_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
202 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Intern
avatar
G
Joined: 01 Jan 2016
Posts: 28
CAT Tests
Re: The events A and B are independent. The probability that event A occu  [#permalink]

Show Tags

New post 28 Mar 2020, 01:06
This the way I solved and went wrong:

Only A = A
Only B = B
Intersection = C
None = D

A+B+C = 0.94

I assumed B+C is what is asked as P(B). However, B+C = 0.34.
While I understand the correct approach, can someone explain why this leads to wrong result?
GMAT Club Bot
Re: The events A and B are independent. The probability that event A occu   [#permalink] 28 Mar 2020, 01:06

The events A and B are independent. The probability that event A occu

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





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