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

 It is currently 19 Sep 2019, 16:22

### 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

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

# The events A and B are independent. The probability that event A occur

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58117
The events A and B are independent. The probability that event A occur  [#permalink]

### Show Tags

10 Jul 2016, 23:58
2
11
00:00

Difficulty:

65% (hard)

Question Stats:

47% (01:03) correct 53% (01:09) wrong based on 187 sessions

### HideShow timer Statistics

The events A and B are independent. The probability that event A occurs is p and the probability that event B occurs is q. Which of the following is equal to the probability that exactly one of the events A and B occurs?

A. p − 2pq
B. q − pq
C. p + q − 2pq
D. p + q − pq
E. p + q

_________________
Intern
Joined: 30 Mar 2016
Posts: 14
Location: India
GMAT 1: 690 Q51 V31
GPA: 3.23
Re: The events A and B are independent. The probability that event A occur  [#permalink]

### Show Tags

11 Jul 2016, 09:43
1
prashant212 wrote:
Bunuel wrote:
The events A and B are independent. The probability that event A occurs is p and the probability that event B occurs is q. Which of the following is equal to the probability that exactly one of the events A and B occurs?

A. p − 2pq
B. q − pq
C. p + q − 2pq
D. p + q − pq
E. p + q

Probability of A occuring = p , Probability of A NOT occuring = 1-p
Probability of B occuring = q , Probability of B not occurring = 1-q

Probability of atleast of one of A and B occuring = 1-(1-p)(1-q) = p+q -pq

D

This is not right. When you consider atleast one, it also means you are considering the possibility of both events occuring, which should be excluded as per the question.

So correct would be A occurs, B doesn't occur and B occurs, A doesn't occur = p(1-q) + q(1-p) = p+q-2pq
Intern
Joined: 21 Jan 2016
Posts: 46
Location: India
GMAT 1: 640 Q44 V34
WE: Manufacturing and Production (Manufacturing)
Re: The events A and B are independent. The probability that event A occur  [#permalink]

### Show Tags

11 Jul 2016, 00:29
2
Bunuel wrote:
The events A and B are independent. The probability that event A occurs is p and the probability that event B occurs is q. Which of the following is equal to the probability that exactly one of the events A and B occurs?

A. p − 2pq
B. q − pq
C. p + q − 2pq
D. p + q − pq
E. p + q

Probability of A occuring = p , Probability of A NOT occuring = 1-p
Probability of B occuring = q , Probability of B not occurring = 1-q

Probability of atleast of one of A and B occuring = 1-(1-p)(1-q) = p+q -pq

D

_________________
GREEN ORANGE YELLOW RED
Intern
Joined: 15 Jun 2014
Posts: 20
Location: India
Schools: XLRI GM"18 (M)
GMAT 1: 680 Q48 V34
GPA: 3.83
Re: The events A and B are independent. The probability that event A occur  [#permalink]

### Show Tags

11 Jul 2016, 03:37
2
I ll go with C

Probability of A happening and B not happrning- p*(1-q)
Probability of B happening and A not happening- q*(1-p)

Exactly 1 of them happening- p*(1-q)+ q*(1-p) = p+q-2pq
Director
Joined: 20 Feb 2015
Posts: 778
Concentration: Strategy, General Management
Re: The events A and B are independent. The probability that event A occur  [#permalink]

### Show Tags

13 Jul 2016, 08:45
P does and q does not or q does and p does not
p(1-q)+q(1-p),
p+q-2pq
Intern
Joined: 23 Jan 2015
Posts: 38
Location: India
Concentration: Operations
WE: Information Technology (Computer Software)
Re: The events A and B are independent. The probability that event A occur  [#permalink]

### Show Tags

13 Jul 2016, 21:12
Bunuel wrote:
The events A and B are independent. The probability that event A occurs is p and the probability that event B occurs is q. Which of the following is equal to the probability that exactly one of the events A and B occurs?

A. p − 2pq
B. q − pq
C. p + q − 2pq
D. p + q − pq
E. p + q

Just to confirm, if we had to find the probability that one of the events A and B occurs (omitted the highlighted text)-
it would have been:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = p+ q- pq

Is this correct?
Intern
Joined: 02 Apr 2018
Posts: 20
GMAT 1: 710 Q50 V34
GPA: 3.51
Re: The events A and B are independent. The probability that event A occur  [#permalink]

### Show Tags

10 Jun 2018, 09:51
Probability of Exactly one of A or B occurring if I write it in Union form:
P(Exactly one occurring) = P(a U b) - P(a n b) = p(a) + p(b) - 2(p(a n b)) = p + q - 2pq(since a and b are independent)
Intern
Joined: 02 Apr 2018
Posts: 20
GMAT 1: 710 Q50 V34
GPA: 3.51
Re: The events A and B are independent. The probability that event A occur  [#permalink]

### Show Tags

10 Jun 2018, 09:52
Anigr16 wrote:
Bunuel wrote:
The events A and B are independent. The probability that event A occurs is p and the probability that event B occurs is q. Which of the following is equal to the probability that exactly one of the events A and B occurs?

A. p − 2pq
B. q − pq
C. p + q − 2pq
D. p + q − pq
E. p + q

Just to confirm, if we had to find the probability that one of the events A and B occurs (omitted the highlighted text)-
it would have been:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = p+ q- pq

Is this correct?

Yes
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 7755
Location: United States (CA)
Re: The events A and B are independent. The probability that event A occur  [#permalink]

### Show Tags

12 Aug 2019, 11:50
Bunuel wrote:
The events A and B are independent. The probability that event A occurs is p and the probability that event B occurs is q. Which of the following is equal to the probability that exactly one of the events A and B occurs?

A. p − 2pq
B. q − pq
C. p + q − 2pq
D. p + q − pq
E. p + q

Because events A and B are independent, the probability that both A and B occur is the product of their individual probabilities, so we have P(A and B) = pq.

Now, note that the event “A only” means that the part of A that includes both A and B happening is not part of this event. Thus, we have:

P(A only) = P(A) - P(A and B) = p - pq.

Similarly, for the event “B only” we see that

P(B only) = P(B) - P(A and B) = q - pq.

Thus, the probability that exactly one event happens (i.e., A only or B only) is equal to

p - pq + q - pq = p + q - 2pq.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 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.

Re: The events A and B are independent. The probability that event A occur   [#permalink] 12 Aug 2019, 11:50
Display posts from previous: Sort by