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505-555 (Easy)|   Probability|                           
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Jill has applied for a job with each of two different companies. What 14 Aug 2018, 21:28
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dave13
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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

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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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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Jill has applied for a job with each of two different companies. What 15 Aug 2018, 05:28
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AbdurRakib
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
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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:)
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Jill has applied for a job with each of two different companies. What 15 Aug 2018, 06:20
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dave13
AbdurRakib
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



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:)
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Hi..

There is no difference in the two..

Independent events..
Events where outcomes of each event is not dependent on other.
For example getting a head on each of the two coins..
P(A∩B)=P(A)*P(B)=1/2*1/2=1/4

Mutually exclusive events.
That is one event cannot occur if second is occurring.
Say getting 1 or 2 in a roll of dice
So P(A∩B)=0 as intersection is 0
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Jill has applied for a job with each of two different companies. What 17 Jun 2019, 17:18
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Let's say Job 1 = A & Job 2 = B
Let's say probability of A happening = P(A) & probability of B happening = P(B)
Let's also say that probability of A not happening = P(A) & probability of B not happening = P(B)

Question asks us to find the probability of A and B, both happening, P(A*B)

1) Statement 1 gives us probability of A and B not happening.
P(A)*P(B) = 0.3
By formula: Event happening + event not happening = 1
P(A or B) + P(A)P(B) = 1
P(A or B) = 1 - P(A))P(B) = 1 - 0.3 = 0.7
But this statement doesn't tell me anything about P(A) or P(B).
Not sufficient.

2) Statement 2 gives us probability of exactly one event happening ==> P(A)P(B) + P(A)P(B) = 0.5
Again, it doesn't tell me anything about P(A) or P(B)
Not sufficient.

Combining the two statements together, we have P(A or B) and P(A)P(B) + P(A)P(B)
By formula, P(A or B) = P(A)P(B) + P(A)P(B) + P(A*B)
0.7 = 0.5 + P(A*B)
P(A*B) = 0.2

Answer is C.
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Jill has applied for a job with each of two different companies. What 06 Feb 2020, 04:53
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This question can be easily solved using the double matrix method:




Show Spoiler
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Jill has applied for a job with each of two different companies. What 07 Jun 2020, 03:50
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Hi experts,

chetan2u, MathRevolution, ScottTargetTestPrep, abhimahna, AaronPond, BrentGMATPrepNow, GMATBusters

Sorry for tagging everyone. Cunning I am I know (1 reply will suffice). I just want to confirm my understanding of the approach after going through the forum.
 

Let the probability of getting the job 1st company be A.
Let the probability of getting the job only from company A be 'a'.
Let the probability of getting the job from the 2nd company be B.
Let the probability of getting the job only from company B be 'b'.
Let the probability of getting the job from both the companies be 'c'.
Let the probability of getting the job from neither company be 'n'.
A = a + c
B = b + c
Find P(A&B) =?
P(A or B) = P(A) + P(B) - P(A&B) =P (a + c) + P(b + c) - P(c) = P(a) + P(b) + P(c)

Statement 1. P(n) = 0.3

P(a) + P(b) + P(c) + 0.3 = 1
P(a) + P(b) + P(c) = 0.7 Not sufficient

Statement 2. P (a) + P(b) = 0.5

P(A or B) = P(a) + P(b) + P(c)

P(A or B) = 0.5 + P(c) Not sufficient

Combining both the statements
0.7 = 0.5 + P(c)
P(c) = 0.2 Therefore, sufficient.

Takeaway: P(event 1 or event 2) = P(event 1) + P(event 2) - P(event 1 & event 2) So this formula basically stems from the Venn diagram consisting of 2 circles. Am I correct?

Thank you.
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Jill has applied for a job with each of two different companies. What 16 Jun 2020, 19:55
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Hate to add to the thread but I must ask - Why can't I utilize the formula 1-(percent of neither)=(percent of both)? I took this approach and landed on A which cleary wasn't correct. Can someone please help?
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Jill has applied for a job with each of two different companies. What 16 Jun 2020, 20:30
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Hate to add to the thread but I must ask - Why can't I utilize the formula 1-(percent of neither)=(percent of both)? I took this approach and landed on A which cleary wasn't correct. Can someone please help?
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When you subtract probability of neither from 1, you will get probability of offer from at least 1 coy.
So this probability will include - p of only say A company, p of only B and p of both A and B.
Whereas we are looking for the value of probability of both A and B.
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Jill has applied for a job with each of two different companies. What 16 Jun 2020, 20:31
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Hi experts,

chetan2u, MathRevolution, ScottTargetTestPrep, abhimahna, AaronPond, BrentGMATPrepNow, GMATBusters

Sorry for tagging everyone. Cunning I am I know (1 reply will suffice). I just want to confirm my understanding of the approach after going through the forum.
 

Let the probability of getting the job 1st company be A.
Let the probability of getting the job only from company A be 'a'.
Let the probability of getting the job from the 2nd company be B.
Let the probability of getting the job only from company B be 'b'.
Let the probability of getting the job from both the companies be 'c'.
Let the probability of getting the job from neither company be 'n'.
A = a + c
B = b + c
Find P(A&B) =?
P(A or B) = P(A) + P(B) - P(A&B) =P (a + c) + P(b + c) - P(c) = P(a) + P(b) + P(c)

Statement 1. P(n) = 0.3

P(a) + P(b) + P(c) + 0.3 = 1
P(a) + P(b) + P(c) = 0.7 Not sufficient

Statement 2. P (a) + P(b) = 0.5

P(A or B) = P(a) + P(b) + P(c)

P(A or B) = 0.5 + P(c) Not sufficient

Combining both the statements
0.7 = 0.5 + P(c)
P(c) = 0.2 Therefore, sufficient.

Takeaway: P(event 1 or event 2) = P(event 1) + P(event 2) - P(event 1 & event 2) So this formula basically stems from the Venn diagram consisting of 2 circles. Am I correct?

Thank you.
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Yes, you are correct in the approach.
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Jill has applied for a job with each of two different companies. What 02 Aug 2021, 16:33
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P(Total) = 1 = P(no offer) + P(Exactly one offer) + P(two offers)
Option 1 implies 0.3 + P(Exactly one offer) + P(two offers) = 1 . INSUFFICIENT
Option 2 implies P(no offer) + 0.5 + P(two offers) = 1. INSUFFICIENT
Together implies 0.3 + 0.5 + P(two offers) = 1 . SUFFICIENT
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Jill has applied for a job with each of two different companies. What 24 Mar 2023, 00:20
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I am also struggling with the wording on this one.

Considering this equation: Pb = 1−Ps−Pt−Pn , in my opinion "exactly one" can mean one of two things:

I) Ps or Pt
She can get an offer from S or T, therefore leading to E, neither statement is sufficient.

II) Ps + Pt
Obviously leading to C.

So, how can we be sure to what the question is referring to?

Cheers
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Jill has applied for a job with each of two different companies. What 17 May 2025, 13:38
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