Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 21 Oct 2013
Posts: 440
Kudos [?]:
1667
[3]
, given: 289

Events A and B are independent and have equal probabilities [#permalink]
Show Tags
27 Feb 2014, 12:18
3
This post received KUDOS
19
This post was BOOKMARKED
Question Stats:
24% (02:16) correct
76% (01:18) wrong based on 357 sessions
HideShow timer Statistics
Events A and B are independent and have equal probabilities of occurring. What is the probability that event A occurs? (1) The probability that at least one of events A and B occurs is 0.84. (2) The probability that event B occurs and event A does not is 0.24. Since A and B have equal probabilities of occurring (Probability p), they have equal probabilities of not occurring. Probability that neither of the events occurs is 0.16 (the complementary probability of 0.84, or 1  0.84). Therefore, probability of A not occurring and probability of B not occurring is 0.16. → (not p)(not p) = 0.16 → (not p)^2 = 0.16 → p = 0.4 If we know probability that event will not occur, then we know probability that it will occur (0.6 = 60%). Statement (1): Sufficient. Statement (2): Probability that event A does not occur is simply (1 – p) p(1 –p) = 0.24 → (p^2 – p + 0.24) = 0, and factoring for 2 numbers that multiply to 0.24 and add to 1 (implicit coefficient in front of p) gives 2 possible values for p: 0.6 & 0.4. Insufficient. Hi, the Statement (1) is not very clear to me. Can anyone explain the exact meaning and why it is Sufficient, please.
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by goodyear2013 on 28 Feb 2014, 07:22, edited 1 time in total.

Kudos [?]:
1667
[3]
, given: 289


Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7567
Kudos [?]:
16419
[7]
, given: 229
Location: Pune, India

Re: Events A and B are independent and have equal probabilities [#permalink]
Show Tags
27 Feb 2014, 21:59
7
This post received KUDOS
Expert's post
11
This post was BOOKMARKED
goodyear2013 wrote: Events A and B are independent and have equal probabilities of occurring. What is the probability that event A occurs? 1: The probability that at least one of events A and B occurs is 0.84. 2: The probability that event B occurs and event A does not is 0.24. Since A and B have equal probabilities of occurring (Probability p), they have equal probabilities of not occurring. Probability that neither of the events occurs is 0.16 (the complementary probability of 0.84, or 1  0.84). Therefore, probability of A not occurring and probability of B not occurring is 0.16. → (not p)(not p) = 0.16 → (not p)^2 = 0.16 → p = 0.4 If we know probability that event will not occur, then we know probability that it will occur (0.6 = 60%). Statement (1): Sufficient. Statement (2): Probability that event A does not occur is simply (1 – p) p(1 –p) = 0.24 → (p^2 – p + 0.24) = 0, and factoring for 2 numbers that multiply to 0.24 and add to 1 (implicit coefficient in front of p) gives 2 possible values for p: 0.6 & 0.4. Insufficient. Hi, the Statement (1) is not very clear to me. Can anyone explain the exact meaning and why it is Sufficient, please. (To me, it does not sound like the Official GMAT question.) Let me take the approach used more often: Assume that P(A) = x. Given that P(B) = P(A) = x P(A and B) = P(A) * P(B) = x^2 (Probability that both occur is product of the two since events are independent) 1: The probability that at least one of events A and B occurs is 0.84. P(A or B) = P(A) + P(B)  P(A and B) = .84 x + x  x^2 = .84 x^2 2x +.84 = 0 100x^2  200x + 84 = 0 This is a quadratic and when you solve it, you get x = 3/5 or 7/5. The probability cannot be more than 1 so x must be 3/5 = 0.6 Sufficient. The method used in the explanation is this: P(A or B) = .84 This means that probability that neither occurs = 1  P(A or B) = .16 P('not A' and 'not B') = P(not A)*P(not B) = P(not A)*P(not A) = .16 (Since P(B) = P(A), P(not B) = P(not A). Also they are independent events so P that both don't occur is product of P(not A) and P(not B) P(not A) = .40 So P(A) = .6 This method is faster and innovative. 2: The probability that event B occurs and event A does not is 0.24. On similar lines, P(B)*P(not A) = 0.24 x(1  x) = .24 x could be 0.6 and 1x would be 0.4 then OR x could be 0.4 and 1x would be 0.6 then. Hence we don't get a unique value for x Not sufficient. Answer (A)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews

Kudos [?]:
16419
[7]
, given: 229


Intern
Joined: 12 Oct 2014
Posts: 4
Kudos [?]:
0
[0], given: 0

Events A and B are independent and have equal probabilities [#permalink]
Show Tags
19 Jul 2015, 17:18
The Statement (2) is not sufficient but I think the explanation is wrong. You can't multiply that way because those probabilities have intersection (not independent).

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


Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2679
Kudos [?]:
1629
[0], given: 792
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: Events A and B are independent and have equal probabilities [#permalink]
Show Tags
19 Jul 2015, 17:29
Andrake26 wrote: The Statement (2) is not sufficient but I think the explanation is wrong. You can't multiply that way because those probabilities have intersection (not independent). The question does mention that the two events, A and B are independent. Thus the intersection is not there. This means, P(A and B) = P (A) * P(B) and P(A or B) = P(A) + P (B). The explanation given by VeritasPrepKarishma is correct.
_________________
Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidatedthursdaywithronlistforallthesections201006.html#p1544515 Rules for Posting in Quant Forums: http://gmatclub.com/forum/rulesforpostingpleasereadthisbeforeposting133935.html Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rulesforpostingpleasereadthisbeforeposting133935.html#p1096628 GMATCLUB Math Book: http://gmatclub.com/forum/gmatmathbookindownloadablepdfformat130609.html Everything Related to Inequalities: http://gmatclub.com/forum/inequalitiesmadeeasy206653.html#p1582891 Inequalities tips: http://gmatclub.com/forum/inequalitiestipsandhints175001.html Debrief, 650 to 750: http://gmatclub.com/forum/650to750a10monthjourneytothescore203190.html

Kudos [?]:
1629
[0], given: 792


Director
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 615
Kudos [?]:
588
[0], given: 298
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49
GPA: 3.3

Re: Events A and B are independent and have equal probabilities [#permalink]
Show Tags
05 Aug 2015, 04:14
VeritasPrepKarishma wrote: goodyear2013 wrote: Events A and B are independent and have equal probabilities of occurring. What is the probability that event A occurs? 1: The probability that at least one of events A and B occurs is 0.84. 2: The probability that event B occurs and event A does not is 0.24. Since A and B have equal probabilities of occurring (Probability p), they have equal probabilities of not occurring. Probability that neither of the events occurs is 0.16 (the complementary probability of 0.84, or 1  0.84). Therefore, probability of A not occurring and probability of B not occurring is 0.16. → (not p)(not p) = 0.16 → (not p)^2 = 0.16 → p = 0.4 If we know probability that event will not occur, then we know probability that it will occur (0.6 = 60%). Statement (1): Sufficient. Statement (2): Probability that event A does not occur is simply (1 – p) p(1 –p) = 0.24 → (p^2 – p + 0.24) = 0, and factoring for 2 numbers that multiply to 0.24 and add to 1 (implicit coefficient in front of p) gives 2 possible values for p: 0.6 & 0.4. Insufficient. Hi, the Statement (1) is not very clear to me. Can anyone explain the exact meaning and why it is Sufficient, please. (To me, it does not sound like the Official GMAT question.) Let me take the approach used more often: Assume that P(A) = x. Given that P(B) = P(A) = x P(A and B) = P(A) * P(B) = x^2 (Probability that both occur is product of the two since events are independent) 1: The probability that at least one of events A and B occurs is 0.84. P(A or B) = P(A) + P(B)  P(A and B) = .84 x + x  x^2 = .84 x^2 2x +.84 = 0 100x^2  200x + 84 = 0 This is a quadratic and when you solve it, you get x = 3/5 or 7/5. The probability cannot be more than 1 so x must be 3/5 = 0.6 Sufficient. The method used in the explanation is this: P(A or B) = .84 This means that probability that neither occurs = 1  P(A or B) = .16 P('not A' and 'not B') = P(not A)*P(not B) = P(not A)*P(not A) = .16 (Since P(B) = P(A), P(not B) = P(not A). Also they are independent events so P that both don't occur is product of P(not A) and P(not B) P(not A) = .40 So P(A) = .6 This method is faster and innovative. 2: The probability that event B occurs and event A does not is 0.24. On similar lines, P(B)*P(not A) = 0.24 x(1  x) = .24 x could be 0.6 and 1x would be 0.4 then OR x could be 0.4 and 1x would be 0.6 then. Hence we don't get a unique value for x Not sufficient. Answer (A) Karishma I think this is the Formula  For Mutually Exclusive events : Those events which will have nothing in common between them. 2 different sample space. P (A or B ) = P(A) + p(B)
_________________
Like my post Send me a Kudos It is a Good manner. My Debrief: http://gmatclub.com/forum/howtoscore750and750imovedfrom710to189016.html

Kudos [?]:
588
[0], given: 298


Jamboree GMAT Instructor
Status: GMAT Expert
Affiliations: Jamboree Education Pvt Ltd
Joined: 15 Jul 2015
Posts: 8
Kudos [?]:
10
[1]
, given: 0
Location: India

Events A and B are independent and have equal probabilities [#permalink]
Show Tags
05 Aug 2015, 05:04
1
This post received KUDOS
goodyear2013 wrote: Events A and B are independent and have equal probabilities of occurring. What is the probability that event A occurs? (1) The probability that at least one of events A and B occurs is 0.84. (2) The probability that event B occurs and event A does not is 0.24. Since A and B have equal probabilities of occurring (Probability p), they have equal probabilities of not occurring. Probability that neither of the events occurs is 0.16 (the complementary probability of 0.84, or 1  0.84). Therefore, probability of A not occurring and probability of B not occurring is 0.16. → (not p)(not p) = 0.16 → (not p)^2 = 0.16 → p = 0.4 If we know probability that event will not occur, then we know probability that it will occur (0.6 = 60%). Statement (1): Sufficient. Statement (2): Probability that event A does not occur is simply (1 – p) p(1 –p) = 0.24 → (p^2 – p + 0.24) = 0, and factoring for 2 numbers that multiply to 0.24 and add to 1 (implicit coefficient in front of p) gives 2 possible values for p: 0.6 & 0.4. Insufficient. Hi, the Statement (1) is not very clear to me. Can anyone explain the exact meaning and why it is Sufficient, please. Hi goodyear2013, statement (1) implies that probability of occurrence of at least one of the two events is 0.84. Hence, the given probability (0.84) includes 3 possibilities: 1. A happens and B does not 2. B happens and A does not 3. A and B both happen In the first case, the probability can be written as P(A)*[1  P(B)]. Similarly, in the second case, probability can be calculated as \([1  P(A)]*P(B)\); and in the third case, probability is P(A)*P(B). This will give the equation as: \(2p(1  p) + {p}^{2} = 0.84\) and value of p (as Karishma explained) will be 3/5. Alternate Method: If we consider all the cases there can be when 2 events do or do not occur, then they are as follows: 1. both A and B occur 2. A occurs and B does not 3. B occurs and A does not 4. both A and B do not occur Hence, addition of the probabilities of the above four cases should be 1. Since the first statement considers the combined probability of the first three cases, thus (1  0.84) should be the probability of fourth case. It implies that 0.16 = (1  p)*(1  p). Hope this explanation helps.

Kudos [?]:
10
[1]
, given: 0


Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7567
Kudos [?]:
16419
[2]
, given: 229
Location: Pune, India

Re: Events A and B are independent and have equal probabilities [#permalink]
Show Tags
06 Aug 2015, 02:50
2
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
honchos wrote: Karishma I think this is the Formula 
For Mutually Exclusive events : Those events which will have nothing in common between them. 2 different sample space. P (A or B ) = P(A) + p(B)
Independent events are not the same as mutually exclusive events. When events are independent, they can both occur at the same time. For example: Team A will win the match tomorrow. It will rain tomorrow. These events are independent. One does not depend on the other but they both can occur tomorrow. P(A or B) = P(A) + P(B)  P(A)*P(B) It will rain less than 1 mm tomorrow. It will rain more than 3 mmm tomorrow. These two events are mutually exclusive and cannot happen at the same time. P(A or B) = P(A) + P(B)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews

Kudos [?]:
16419
[2]
, given: 229


GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17108
Kudos [?]:
261
[0], given: 0

Re: Events A and B are independent and have equal probabilities [#permalink]
Show Tags
12 Oct 2016, 17:50
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 Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources

Kudos [?]:
261
[0], given: 0


Manager
Joined: 13 Apr 2017
Posts: 63
Kudos [?]:
2
[0], given: 2

Re: Events A and B are independent and have equal probabilities [#permalink]
Show Tags
14 Apr 2017, 13:13
the problem is just another a simple equation

Kudos [?]:
2
[0], given: 2



Re: Events A and B are independent and have equal probabilities
[#permalink]
14 Apr 2017, 13:13







