Events A and B are independent and have equal probabilities : Data Sufficiency (DS)

Andrake26

Joined: 12 Oct 2014

Last visit: 22 May 2025

Posts: 5

Own Kudos:

1

[1]

Posts: 5

Kudos: 1

[1]

19 Jul 2015, 17:18

1

Kudos

Bookmarks

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).

ENGRTOMBA2018

Joined: 20 Mar 2014

Last visit: 01 Dec 2021

Posts: 2,328

Own Kudos:

3,787

Given Kudos: 816

Concentration: Finance, Strategy

Schools: Kellogg '18 (M)

GMAT 1: 750 Q49 V44 Verified score

GPA: 3.7

WE:Engineering (Aerospace and Defense)

Products:

Schools: Kellogg '18 (M)

GMAT 1: 750 Q49 V44 Verified score

Posts: 2,328

Kudos: 3,787

19 Jul 2015, 17:29

Kudos

Bookmarks

Andrake26

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.

honchos

Joined: 17 Apr 2013

Last visit: 30 Aug 2021

Posts: 360

Own Kudos:

2,398

[1]

Given Kudos: 298

Status:Verbal Forum Moderator

Location: India

GMAT 1: 710 Q50 V36 Verified score

GMAT 2: 750 Q51 V41 Verified score

GMAT 3: 790 Q51 V49 Verified score

GPA: 3.3

GMAT 3: 790 Q51 V49 Verified score

Posts: 360

Kudos: 2,398

[1]

05 Aug 2015, 04:14

Kudos

1

Bookmarks

VeritasPrepKarishma

goodyear2013

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.

Show Spoiler

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 1-x would be 0.4 then OR x could be 0.4 and 1-x 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)

SKMishra

Jamboree GMAT Instructor

Joined: 15 Jul 2015

Last visit: 17 Jul 2020

Posts: 6

Own Kudos:

16

[5]

Status:GMAT Expert

Affiliations: Jamboree Education Pvt Ltd

Location: India

GMAT 1: 680 Q51 V28 Verified score

Posts: 6

Kudos: 16

[5]

05 Aug 2015, 05:04

5

Kudos

Bookmarks

goodyear2013

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.

Show Spoiler

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.

chessgiants

Joined: 13 Apr 2017

Last visit: 23 Jan 2018

Posts: 33

Own Kudos:

5

Given Kudos: 2

Posts: 33

Kudos: 5

14 Apr 2017, 13:13

Kudos

Bookmarks

the problem is just another a simple equation

GMATBusters

GMAT Tutor

Joined: 27 Oct 2017

Last visit: 20 Jun 2025

Posts: 1,926

Own Kudos:

6,417

Given Kudos: 241

WE:General Management (Education)

Expert

Expert reply

Posts: 1,926

Kudos: 6,417

20 Jul 2018, 22:53

Kudos

Bookmarks

Since A and B have equal probabilities of occurring (let’s call that probability p), they also have equal probabilities of not occurring. The probability that neither of the events occurs is .16 (the complementary probability of .84, or 1 - .84). Therefore, the probability of A not occurring and the probability of B not occurring is .16.
That means that (not p)(not p) = .16, or \((not p)^2\) = .16.

Take the square root of both sides to find that the probability of an event not occurring is .4. If we know the probability that an event will not occur, then we know the probability that it will occur (in this case, it is .6, or 60%).
So Statement (1) is sufficient.

Statement (2): The probability that event A does not occur is simply 1 – p, so Statement (2) gives us p(1 – p) = .24. This quadratic becomes \(p^2 - p + .24 = 0\), and factoring for two numbers that multiply to .24 and add to -1 (the implicit coefficient in front of p) gives us two possible values for p: .6 and .4.
So Statement (2) alone is insufficient.

The correct answer is therefore (A).

mdhyan2012

Joined: 27 Dec 2016

Last visit: 19 Aug 2022

Posts: 8

Own Kudos:

29

Given Kudos: 223

Posts: 8

Kudos: 29

31 Aug 2020, 18:48

Kudos

Bookmarks

VeritasKarishma

goodyear2013

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.

Show Spoiler

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 1-x would be 0.4 then OR x could be 0.4 and 1-x would be 0.6 then. Hence we don't get a unique value for x
Not sufficient.

Answer (A)

Hi,

But if you consider the case in which both A and B are disjoint, then statement 1 by itself won't be sufficient.

So I think the answer is E.

Thanks

CEdward

Joined: 11 Aug 2020

Last visit: 14 Apr 2022

Posts: 1,212

Own Kudos:

247

Given Kudos: 332

Posts: 1,212

Kudos: 247

13 Feb 2021, 21:16

Kudos

Bookmarks

VeritasKarishma

goodyear2013

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.

Show Spoiler

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 1-x would be 0.4 then OR x could be 0.4 and 1-x would be 0.6 then. Hence we don't get a unique value for x
Not sufficient.

Answer (A)

I think this is where I got confused with statement 1. I interpreted "The probability that at least one of events A and B" as the following probability:

P(A or B or both) rather than ...

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

VeritasKarishma can you clarify?

KarishmaB

Tutor

Joined: 16 Oct 2010

Last visit: 14 Jul 2025

Posts: 16,106

Own Kudos:

74,320

[4]

Given Kudos: 475

Location: Pune, India

Expert

Expert reply

Posts: 16,106

Kudos: 74,320

[4]

16 Feb 2021, 00:08

3

Kudos

1

Bookmarks

CEdward

VeritasKarishma

goodyear2013

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.

Show Spoiler

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 1-x would be 0.4 then OR x could be 0.4 and 1-x would be 0.6 then. Hence we don't get a unique value for x
Not sufficient.

Answer (A)

I think this is where I got confused with statement 1. I interpreted "The probability that at least one of events A and B" as the following probability:

P(A or B or both) rather than ...

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

VeritasKarishma can you clarify?

P(A or B) is the same as P(A or B or Both). When we say P(A or B), we mean to say 'probability that A happens or B happens or both happen' i.e. at least one of them does take place and both could also take place.

P(A or B) = P(A) + P(B) - P(Both)
includes the case where Both take place. We subtract P(Both) above because it is counted twice, once in P(A) and then in P(B). But we need to count it only once.

dave13

Joined: 09 Mar 2016

Last visit: 23 Nov 2024

Posts: 1,114

Own Kudos:

1,087

Given Kudos: 3,851

Posts: 1,114

Kudos: 1,087

20 Jun 2021, 06:03

Kudos

Bookmarks

VeritasKarishma

goodyear2013

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.

Show Spoiler

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 1-x would be 0.4 then OR x could be 0.4 and 1-x would be 0.6 then. Hence we don't get a unique value for x
Not sufficient.

Answer (A)

VeritasKarishma how did you get this x(1 - x) = .24 from this P(B)*P(not A) = 0.24

KarishmaB

Tutor

Joined: 16 Oct 2010

Last visit: 14 Jul 2025

Posts: 16,106

Own Kudos:

74,320

[1]

Given Kudos: 475

Location: Pune, India

Expert

Expert reply

Posts: 16,106

Kudos: 74,320

[1]

20 Jun 2021, 22:47

1

Kudos

Bookmarks

dave13

VeritasKarishma

goodyear2013

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.

Show Spoiler

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 1-x would be 0.4 then OR x could be 0.4 and 1-x would be 0.6 then. Hence we don't get a unique value for x
Not sufficient.

Answer (A)

VeritasKarishma how did you get this x(1 - x) = .24 from this P(B)*P(not A) = 0.24

Events A and B are independent and have equal probabilities of occurring.

So say P(A) = x
P(not A) = 1 - x (Complementary event of A)

P(B) = x (because not events have equal probability of occurring)
P(not B) = 1 - x (Complementary event of B)

Given:
P(B)*P(not A) = 0.24
x * (1 - x) = 0.24

dave13

Joined: 09 Mar 2016

Last visit: 23 Nov 2024

Posts: 1,114

Own Kudos:

1,087

Given Kudos: 3,851

Posts: 1,114

Kudos: 1,087

21 Jun 2021, 02:04

Kudos

Bookmarks

Quote:

Events A and B are independent and have equal probabilities of occurring.

So say P(A) = x
P(not A) = 1 - x (Complementary event of A)

P(B) = x (because not events have equal probability of occurring)
P(not B) = 1 - x (Complementary event of B)

Given:
P(B)*P(not A) = 0.24
x * (1 - x) = 0.24

VeritasKarishma thanks, just one question:

Probability of A and B are equal, say A= 1/4 and B =1/4

then as per your explanation i get 1/4 -1

also "1" in probability of indepedent events implies this p(a)+p(b)-both+neither isnt it so ?

now whats wrong with my reasoning

IanStewart

GMAT Tutor

Joined: 24 Jun 2008

Last visit: 14 Jul 2025

Posts: 4,142

Own Kudos:

10,623

[1]

Given Kudos: 97

Q51 V47

Expert

Expert reply

Posts: 4,142

Kudos: 10,623

[1]

21 Jun 2021, 02:55

1

Kudos

Bookmarks

dave13

Probability of A and B are equal, say A= 1/4 and B =1/4

then as per your explanation i get 1/4 -1

also "1" in probability of indepedent events implies this p(a)+p(b)-both+neither isnt it so ?

As Karishma said, if the probability A happens is x, the probability A does not happen is 1-x. If x = 1/4, then the probability A does not happen is 1 - (1/4) = 3/4 (it is not 1/4 - 1).

The formula you write out is just a Venn diagram formula, so it will always be correct provided you have a Venn situation, though I've never used it to answer a GMAT probability question. If as you suggest P(A) = 1/4, then P(B) = 1/4 (the probabilities are equal in this question), P(both) = (1/4)(1/4) = 1/16, and P(neither) = (3/4)(3/4) = 9/16. If you now plug into your formula, you will indeed get 1 as the result: 1/4 + 1/4 - 1/16 + 9/16 = 1.

bumpbot

Non-Human User

Joined: 09 Sep 2013

Last visit: 04 Jan 2021

Posts: 37,398

Own Kudos:

1,013

Posts: 37,398

Kudos: 1,013

20 May 2025, 06:34

Kudos

Bookmarks

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.

Events A and B are independent and have equal probabilities

Prep Toolkit

My Rewards

GMAT Data Sufficiency (DS) Questions

Events A and B are independent and have equal probabilities

Prep Toolkit

My Rewards