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Jill has applied for a job with each of two different companies. What

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New post 15 Jun 2016, 03:27
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Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3
2) The probability that she will get a job offer from exactly one of the two companies is 0.5

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New post 16 Jun 2016, 20:09
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rahulkashyap wrote:
chetan2u pls help with this

Posted from my mobile device


Hi Rahul,

Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3
2) The probability that she will get a job offer from exactly one of the two companies is 0.5

\(P_b\)= probability that she will get job offers from both companies
\(P_s\) = probability that she will get job offer ONLY from 's' company, one of the 2 companies
\(P_t\) = probability that she will get job offer ONLY from 't' company, second of the 2 companies
\(P_n\) = probability that she will get job offer from 'none' of the companies....

\(P_b = 1-P_s-P_t-P_n\)
so we require to know the values for \(P_s,P_t\) and \(P_n\)...

lets see the statements now-

1) The probability that she will get a job offer from neither company is 0.3
this gives us \(P_n\), But we require to know \(P_s\)and \(P_t\)
Insuff

2) The probability that she will get a job offer from exactly one of the two companies is 0.5
this gives us \(P_s + P_t\), but we do not know \(P_n\)...
Insuff

Combined-
we know all the variables to answer the Q....
\(P_b = 1-P_s-P_t-P_n...................P_b = 1-0.5-0.3=0.2\)
Suff
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New post Updated on: 02 Jan 2018, 10:58
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Here's a visual solution to this question:


Originally posted by GMATAcademy on 30 Jun 2016, 10:02.
Last edited by Bunuel on 02 Jan 2018, 10:58, edited 1 time in total.
Edited.
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Re: Jill has applied for a job with each of two different companies. What  [#permalink]

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New post 16 Jun 2016, 13:45
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AbdurRakib wrote:
Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3
2) The probability that she will get a job offer from exactly one of the two companies is 0.5

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There are four possibilities or elements

1) Get the call from 1st company
2) Get the call from 2nd company
3) Get call from both companies
4) do not get call from any of the companies

And all these possibilities must add to give 1 as a result

Statement 1
1) The probability that she will get a job offer from neither company is 0.3

i.e the 4th element is 0.3

but, we don't know about the remaining 3. Hence, not sufficient.

Statement 2:-

2) The probability that she will get a job offer from exactly one of the two companies is 0.5
either element 1 or 2 is .5

but, we still do not know the other values. Hence, not sufficent.

Combining both statements.
assume that probability of other company to give offer is x.

Now, as we inferred before starting analyzing the statement:-

x+.5+.5x+.3= 1

we can find x and .5x from this equation. Hence, sufficient. C is the answer
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Re: Jill has applied for a job with each of two different companies. What  [#permalink]

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New post 16 Jun 2016, 20:15
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Divyadisha wrote:
AbdurRakib wrote:
Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3
2) The probability that she will get a job offer from exactly one of the two companies is 0.5

OG 2017 New Question


There are four possibilities or elements

1) Get the call from 1st company
2) Get the call from 2nd company
3) Get call from both companies
4) do not get call from any of the companies

And all these possibilities must add to give 1 as a result

Statement 1
1) The probability that she will get a job offer from neither company is 0.3

i.e the 4th element is 0.3

but, we don't know about the remaining 3. Hence, not sufficient.

Statement 2:-

2) The probability that she will get a job offer from exactly one of the two companies is 0.5
either element 1 or 2 is .5


but, we still do not know the other values. Hence, not sufficent.

Combining both statements.
assume that probability of other company to give offer is x.

Now, as we inferred before starting analyzing the statement:-

x+.5+.5x+.3= 1

we can find x and .5x from this equation. Hence, sufficient. C is the answer


Hi Divyadisha,

Your approach has been correct but the inference from statement 2 is not correct.
2) The probability that she will get a job offer from exactly one of the two companies is 0.5 either element 1 or 2 is .5
this does not mean that Prob for one is x and for other is 0.5x...
It means the prob of calls from two coys MINUS the overlap that is CALL from both is 0.5
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Re: Jill has applied for a job with each of two different companies. What  [#permalink]

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New post 16 Jun 2016, 20:58
Consider two companies as A and B.
There are 4 variables (P(A),P(B),P(intersection of A and B), P(~AUB) and 1 equation (P(A)+P(B)-P(intersection of A and B)+P(~AUB))=1) in the original condition. Hence, we need 3 equations, which makes E likely the answer.
Using the condition 1) and the condition 2), from P(A-B)+P(B-A)=0.5 we and P(~AUB)=0.3, we get P(intersection between A and B)=0.2. Hence, the answer is unique and the condition is sufficient. Thus, the correct answer is C.
(This is only true to the probability of getting offer in P(A-B)=A. We exclude the possibility of job offers from B)

- For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Re: Jill has applied for a job with each of two different companies. What  [#permalink]

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New post 30 Jun 2016, 21:33
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Hello folks, here is my solution. The problem is very good and required some thinking.
The question asks the probability of getting selected by both companies A and B.
1) stat #1 - the probability of getting call from neither = 0.3
We can infer that prob of getting call from either companies = 1-0.3 = 0.7. So there is a good a chance of 0.7 that the person will get call from at least one of the companies.

2) stat #2 - Prob of getting a call from exactly one company = 0.5. This implies that Prob(A said yes but B said no) + Prob(Bsaid yes but A said no) = 0.5.
But with this alone we cant get info of both saying yes. So not suff

Now Prob(A yes but B no)+ Prob(B yes but A no)+Prob(A and B yes) = Prob(at least one says yes).
0.5+Prob(A and B yes) = 0.7.. so we can solve this and this is sufficient
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New post Updated on: 31 Aug 2016, 09:42
1
AbdurRakib wrote:
Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3
2) The probability that she will get a job offer from exactly one of the two companies is 0.5

OG 2017 New Question


This is a question about non exclusive events.
We should have info about 4 events
Job offer from Only company A
Job offer from Only company B
Job offer from BOTH companies A and B
Job offer from Neither company A or Company B
Think of it in terms of set theory with two over lapping sets. {SEE ATTACHED DIAGRAM}

1) The probability that she will get a job offer from neither company is 0.3
We do not probability of job offer from both ,or job offer from one
INSUFFICIENT

2) The probability that she will get a job offer from exactly one of the two companies is 0.5
We do not probability of job offer from both company or probability of job offer from neither
INSUFFICIENT

MERGING both statements
WE know probablity of :- job offer from none and job offer from one company
We still dont know the probablity of job offer from second company

INSUFFICIENT
ANSWER IS E
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Originally posted by LogicGuru1 on 04 Aug 2016, 05:08.
Last edited by LogicGuru1 on 31 Aug 2016, 09:42, edited 1 time in total.
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Re: Jill has applied for a job with each of two different companies. What  [#permalink]

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New post 31 Aug 2016, 07:05
1
LogicGuru1 wrote:
AbdurRakib wrote:
Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3
2) The probability that she will get a job offer from exactly one of the two companies is 0.5

OG 2017 New Question


This is a question about non exclusive events.
We should have info about 4 events
Job offer from company A
Job offer from company A
Job offer from both companies A and B
Job offer from None
Think of it in terms of set theory with two over lapping sets. {SEE ATTACHED DIAGRAM}

1) The probability that she will get a job offer from neither company is 0.3
We do not probability of job offer from both ,or job offer from one
INSUFFICIENT

2) The probability that she will get a job offer from exactly one of the two companies is 0.5
We do not probability of job offer from both company or probablity of job offer from neither
INSUFFICIENT

MERGING both statements
WE know probablity of :- job offer from none and job offer from one company
We still dont know the probablity of job offer from second comapny

INSUFFICIENT
ANSWER IS E

Quote:
Your approach is correct, but answer is wrong.
Stmt 2 -- exactly one of the two companies is 0.5 === It can be from A or B.
From Stmt1, we have N==Neither, so we get something = A or B or AnB
So, we can calculate,
AUB = A +B - AnB +N


So, Ans is C
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New post 31 Aug 2016, 09:38
yosita18 wrote:
LogicGuru1 wrote:
AbdurRakib wrote:
Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3
2) The probability that she will get a job offer from exactly one of the two companies is 0.5

OG 2017 New Question


This is a question about non exclusive events.
We should have info about 4 events
Job offer from company A
Job offer from company A
Job offer from both companies A and B
Job offer from None
Think of it in terms of set theory with two over lapping sets. {SEE ATTACHED DIAGRAM}

1) The probability that she will get a job offer from neither company is 0.3
We do not probability of job offer from both ,or job offer from one
INSUFFICIENT

2) The probability that she will get a job offer from exactly one of the two companies is 0.5
We do not probability of job offer from both company or probablity of job offer from neither
INSUFFICIENT

MERGING both statements
WE know probablity of :- job offer from none and job offer from one company
We still dont know the probablity of job offer from second comapny

INSUFFICIENT
ANSWER IS E

Quote:
Your approach is correct, but answer is wrong.
Stmt 2 -- exactly one of the two companies is 0.5 === It can be from A or B.
From Stmt1, we have N==Neither, so we get something = A or B or AnB
So, we can calculate,
AUB = A +B - AnB +N


So, Ans is C


Oops ... My bad .. :oops: yes the correct answer is C
I see I made a mistake in interpreting statement B in conjunction with the stimulus

The answer is indeed C
Thanks for pointing out the error. :)
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Re: Jill has applied for a job with each of two different companies. What  [#permalink]

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New post 06 Dec 2016, 17:50
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AbdurRakib wrote:
Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3
2) The probability that she will get a job offer from exactly one of the two companies is 0.5


Let’s say Jill is applying to company A and company B. We can create the following equation:

1 = P(offer from only A) + P(offer from only B) + P(offer from both) + P(offer from neither)

We need to determine the probability that she will get a job offer from both companies.

Statement One Alone:

The probability that she will get a job offer from neither company is 0.3.

Statement one tells us that P(offer from neither) = 0.3; however, we still need to know P(offer from only A) + P(offer from only B) to determine P(offer from both). Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The probability that she will get a job offer from exactly one of the two companies is 0.5.

Statement two tells us that P(offer from only A) + P(offer from only B) = 0.5; however, we still need to know P(offer from neither) to determine P(offer from both). We can eliminate answer choice B.

Statements One and Two Together:

Using the information in statements one and two, we know the following:

P(offer from neither) = 0.3

P(offer from only A) + P(offer from only B) = 0.5

Thus:

1 = 0.5 + P(offer from both) + 0.3

0.2 = P(offer from both)

Answer: C
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New post 25 Mar 2017, 19:51
I tried using the formula P(A or B) = P(A) + P(B) - P(A & B) here but didn't quite get it to work out, any help?
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Re: Jill has applied for a job with each of two different companies. What  [#permalink]

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New post 04 May 2017, 19:19
Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3
2) The probability that she will get a job offer from exactly one of the two companies is 0.5

My 2 cents.
Plug in number.

1)
Job A No Job A Total
Job B : ? / /
No Job B : / 0.3 /
Total : / / 1

Certainly insufficient.

2)

Job A No Job A Total
Job B : ? / / 0.5
No Job B : / / 0.5
Total : 0.5 / 0.5 / 1

Insufficient.

Lets combine

Job A No Job A Total
Job B : 0.3 / 0.2 / 0.5
No Job B : 0.2 / 0.3 / 0.5
Total : 0.5 / 0.5 / 1

C.
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Re: Jill has applied for a job with each of two different companies. What  [#permalink]

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New post 26 Jul 2017, 13:41
1 = P(offer from only A) + P(offer from only B) + P(offer from both) + P(offer from neither)

Where does this formula come from?

I keep confusing this with ---> Total = X + Y - Both + Neither

Is there a relationship between them? How are these derived?
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New post 28 Jul 2017, 00:30
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TheMastermind wrote:
1 = P(offer from only A) + P(offer from only B) + P(offer from both) + P(offer from neither)

Where does this formula come from?

I keep confusing this with ---> Total = X + Y - Both + Neither

Is there a relationship between them? How are these derived?


Hi TheMastermind ,

These formulas are actually the same.

Total Probability - Probability(Neither A nor B) = Probability(only A) + Probability(only B) + Probability(both A and B).

Total probability is always 1.

I know you are getting confused with Venn Diagrams formula.

For example:

People who drink tea may include people who drink coffee Or when I am saying people who drink coffee , I can say these people may include people who drink tea. So, since such people are included twice, I subtract both scenario ones.

When I don't know the individual only occurrences, I use, Total - Neither= X + Y - Both

When I know individual only occurrences, I can write my Venn diagram formula like this:

Total = Only A + Only B + Both A and B. [Note that this time I am not including people who drink both even a single time. Hence, I need to add that once.]

Look at the diagram made by LogicGuru1 above. You will understand what I am saying.

Does that make sense?
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Re: Jill has applied for a job with each of two different companies. What  [#permalink]

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New post 02 Jun 2018, 00:15
Hence getting job from either company is an independent event, Can't we multiply the probability of getting exactly one job i.e. 0.5 with 0.5 resulting the p(A)p(B)=0.25 so ans B?
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Re: Jill has applied for a job with each of two different companies. What  [#permalink]

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New post 02 Jun 2018, 03:07
Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3
2) The probability that she will get a job offer from exactly one of the two companies is 0.5


Ans: C

Details:
Let's say, Two companies P & Q
Mathematical details From Q: P(P and Q) = ?

1) She will get Job offer from A or from B or from both P & Q: P(P or Q)
> job offer from neither company is 0.3
>> 1- P(P or Q ) = 0.3
>> P(P or Q) = 0.7
>> P(P) + P(Q) - P(P and Q) = 0.7
Unable to find P(P and Q), choices A & D out

2) The probability that she will get a job offer from exactly one of the two companies is 0.5
Job offer only from P = P(P) - P(P and Q)
Job offer only from Q = P(Q) - P(P and Q)
Job offer from exactly one of the two companies is 0.5 = Job offer only from P + Job offer only from Q = P(P) + P(Q) - 2*P(P and Q) =0.5
Unable to find P(P and Q), choices Bout

1) + 2) :
P(P) + P(Q) - P(P and Q) = 0.7 ..........(1)
P(P) + P(Q) - 2*P(P and Q) =0.5 .......(2)
P(P and Q) = 0.2
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New post 14 Aug 2018, 06:22
ScottTargetTestPrep wrote:
AbdurRakib wrote:
Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3
2) The probability that she will get a job offer from exactly one of the two companies is 0.5


Let’s say Jill is applying to company A and company B. We can create the following equation:

1 = P(offer from only A) + P(offer from only B) + P(offer from both) + P(offer from neither)

We need to determine the probability that she will get a job offer from both companies.

Statement One Alone:

The probability that she will get a job offer from neither company is 0.3.

Statement one tells us that P(offer from neither) = 0.3; however, we still need to know P(offer from only A) + P(offer from only B) to determine P(offer from both). Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The probability that she will get a job offer from exactly one of the two companies is 0.5.

Statement two tells us that P(offer from only A) + P(offer from only B) = 0.5; however, we still need to know P(offer from neither) to determine P(offer from both). We can eliminate answer choice B.

Statements One and Two Together:

Using the information in statements one and two, we know the following:

P(offer from neither) = 0.3

P(offer from only A) + P(offer from only B) = 0.5

Thus:

1 = 0.5 + P(offer from both) + 0.3

0.2 = P(offer from both)

Answer: C



it says: The probability that she will get a job offer from exactly one of the two companies is 0.5 .

Doesnt it mean that A company job offer is \(\frac{1}{2}\)and B company job offer is \(\frac{1}{2}\) :?

Why here A+b equal to 0.5 , and not 0.5+0.5

P(offer from only A) + P(offer from only B) = 0.5


pushpitkc are you around ? :-)

Probus maybe you know :-)
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Jill has applied for a job with each of two different companies. What  [#permalink]

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New post 14 Aug 2018, 21:28
3
dave13 wrote:
ScottTargetTestPrep wrote:
AbdurRakib wrote:
Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3
2) The probability that she will get a job offer from exactly one of the two companies is 0.5


Let’s say Jill is applying to company A and company B. We can create the following equation:

1 = P(offer from only A) + P(offer from only B) + P(offer from both) + P(offer from neither)

We need to determine the probability that she will get a job offer from both companies.

Statement One Alone:

The probability that she will get a job offer from neither company is 0.3.

Statement one tells us that P(offer from neither) = 0.3; however, we still need to know P(offer from only A) + P(offer from only B) to determine P(offer from both). Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The probability that she will get a job offer from exactly one of the two companies is 0.5.

Statement two tells us that P(offer from only A) + P(offer from only B) = 0.5; however, we still need to know P(offer from neither) to determine P(offer from both). We can eliminate answer choice B.

Statements One and Two Together:

Using the information in statements one and two, we know the following:

P(offer from neither) = 0.3

P(offer from only A) + P(offer from only B) = 0.5

Thus:

1 = 0.5 + P(offer from both) + 0.3

0.2 = P(offer from both)

Answer: C



it says: The probability that she will get a job offer from exactly one of the two companies is 0.5 .

Doesnt it mean that A company job offer is \(\frac{1}{2}\)and B company job offer is \(\frac{1}{2}\) :?

Why here A+b equal to 0.5 , and not 0.5+0.5

P(offer from only A) + P(offer from only B) = 0.5


pushpitkc are you around ? :-)

Probus maybe you know :-)



Hi dave13,

Well if you are aware of the two set theory, it would be simple to visualize Set A as Company M and Set B as comapnay N

So in two set theory we have
Only A=a, Only B=b, Both A&B=x, neither=n and total=T.
Where Total= only A + Only B +A&B+ n
T=a+x+b+n

Set A= only A and A&B = a+x
Set B= only B and A&B= b+x
Both A&bB=x
or
you also want to remember the other form.
Total= Set A +Set B -Both A&B +neither
T= (a+x)+(b+x)-x+n
which is precisely
T=a+x+b+n.

Now coming back to this question
We know that total =1 . Why you may ask. Probability of any event occurring lies between o and 1
We generally say Probability of an event happening + probability of event not happening =1
We are supposed to find the value of x. What will help us reach that.

T-a-b-n=x
1-a-b-n=x
or
Set A+Set B+n -Total= Both

Either we are given Set A, & Set B and Neither.
or
We are given the values of only A Only B and neither.

So statements 1: We are given the value of n and but in absence of any other information this no way leads us to our goal.So INSUFFICIENT

So statements 2: This gives us a lot of information about only A=a and only B=b . Great but we do need the value of neither to calculate both. So INSUFFICIENT

Why does this statement give information about only A , Only B. In mathematics OR represents addition , AND represents multiplication. We are told that she gets job offer from exactly one. What are the elements that represent exactly one only a , only b. This means she gets job offer from only a OR she gets jobs offer from only B

then only a or only b=0.5
this means that only a+only b =0.5


Now since we know what all information is given in two statements, surely should we combine them we get the values of only A=a,only B=b, neither =n
from this
1-a-b-n=x
1-(0.5)-(0.3)=x
or x= 0.2
Hence both statements are required to find the value of "BOTH" which is asked in question So C is sufficient to answer the question

Probus
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Re: Jill has applied for a job with each of two different companies. What  [#permalink]

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New post 15 Aug 2018, 05:28
AbdurRakib wrote:
Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3
2) The probability that she will get a job offer from exactly one of the two companies is 0.5

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hello Bunuel chetan2u, pushpitkc :-)

could you please give me an example/ problem based on this formula P(A∪B) = P(A)+P(B)-P(A)*P(B)) I want to see how it differs from this one
P(A∪B) = P(A)+P(B)-P(A∩B)

thank you:)
GMAT Club Bot
Re: Jill has applied for a job with each of two different companies. What   [#permalink] 15 Aug 2018, 05:28

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