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Math Expert V
Joined: 02 Aug 2009
Posts: 8004
Jill has applied for a job with each of two different companies. What  [#permalink]

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1
dave13 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

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:)

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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Joined: 11 Sep 2013
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Concentration: Finance, Finance
Re: Jill has applied for a job with each of two different companies. What  [#permalink]

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P(A)+ P(B) - P(A&B)+ neither = 1

0.5 - P(A&B) + 0.3 = 1 ( from st 2, we get the value of P(A)+ P(B) =0.5)

P(A&B) =0.2

Ans C
Manager  S
Joined: 11 Sep 2013
Posts: 131
Concentration: Finance, Finance
Re: Jill has applied for a job with each of two different companies. What  [#permalink]

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P(A) +P(B) - P(A&B) +Neither = 1

0.5- P(A&B) +0.3 =1 ( From St2 we get the value of P(A) +P(B) = 0.5)

P(A&B) = 0.2

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

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A tip: Don't mess with formulas in this kind of questions. Use Venn diagrams - make your life easier. The guy above has uploaded a good video.
Veritas Prep GMAT Instructor G
Joined: 01 Jul 2017
Posts: 79
Location: United States
Concentration: Leadership, Organizational Behavior
Re: Jill has applied for a job with each of two different companies. What  [#permalink]

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There are a lot of explanations on this forum that focus blindly on the math. But remember: the GMAT is a critical-thinking test. Let's talk strategy here. For those of you studying for the GMAT, you will want to internalize strategies that actually minimize the amount of math that needs to be done, making it easier to manage your time. The tactics I will show you here will be useful for numerous questions, not just this one. My solution is going to walk through not just what the answer is, but how to strategically think about it. Ready? Here is the full "GMAT Jujitsu" for this question:

The first strategic leverage we need to recognize for this problem is that we are dealing with a two-group Venn diagram. Jill could get a job offer from both companies, from one of the two companies, or from neither company. Whenever I realize I am dealing with Venn diagrams, I always draw out the overlapping groups. Visualizing these questions is often the key to unlocking them. See the attached image at the bottom of this solution for this visualization.

We can also begin anticipating one of the strategies of Data Sufficiency questions with Venn diagrams. The basic equation for a two-group Venn Diagram is $$T = A + B – M + N$$. This equation assumes that “$$A$$” and “$$B$$” refer to the entire groups, so that we double-count “$$M$$” when we add the groups together. If the problem gives us “only $$A$$” and “only $$B$$”, then we are not double-counting “$$M$$” and the formula would be $$T = A + B + M + N$$. You need to always watch for this distinction in Venn diagram questions.

Many questions creatively combine or eliminate variables so you don’t always need to know all 5 of these values. Always look for large chunks of equations you can cancel or simplify all at once. With systems of equations with multiple variables, look for ways to cancel out numerous variables simultaneously. In my classes, I call this strategy “Chunky-quations.” (The name is a amalgamation of the words "chunky" and "equation".)

Our clear target for this problem is “$$M$$” – the probability that Jill will get an offer from both companies. Statement #1 tells us that the probability that she will get a job offer from neither company is $$0.3$$. Thus, $$N=0.3$$ and the probability that she will get some kind of job offer is $$0.7$$. But the problem isn't asking us for the probability of "some kind" of job offer. There is no reason to do additional math here. We are not sure of the overlap ($$M$$). It is possible that both companies love Jill so much that they will both offer her the job. But it is also possible that there is very little overlap. Because we can think of two situations that follow the constraints of the problem but that give different answers to the question, we know that the statement is not sufficient. Eliminate Statement #1.

Statement #2 is a classic “Chunky-quations” idea – it gives a value for the sum of two groups, telling us that we know the probability of Jill getting a job offer from “exactly one of the two companies is $$0.5$$.” The leverage phrase “exactly” indicates that we are looking at this Venn diagram not from the perspective of overlapping groups, but additive groups. With the formula $$T = A + B + M + N$$, this means that $$A+B = 0.5$$. However, since we don’t know what the “neither” group ($$N$$) is, we don’t have enough information to solve for $$M$$. Statement #2 is insufficient.

Combining the two statements, however, gives us the information we need. If $$N=0.3$$ and $$A+B=0.5$$, we can solve for “$$M$$”. (After all, the total “$$T$$” is $$100\%$$ or “$$1$$”.) We know everything we need to know. $$1 = 0.5 + M + 0.3$$, and $$M = 0.2$$. (Though it might be worthy to mention here that we don’t even need to do this math. Save a few seconds. They add up over time. With Data Sufficiency, soon as you have enough information to conclude that a statement is either sufficient or insufficient, you can move on. Many people spend too much time on Data Sufficiency questions because they think they need to get to the bitter end. You don’t.)

The answer is “C”.

Now, let’s look back at this problem from the perspective of strategy. Your job as you study for the GMAT isn't to memorize the solutions to specific questions; it is to internalize strategic patterns that allow you to solve large numbers of questions. This problem can teach us patterns seen throughout the GMAT. First, when using Venn diagrams, be very conscious of how the groups overlap. There is a profound difference between “Group A” and “only in Group A.” Second, watch for those “Chunky-quations” – the ways the GMAT combines large chunks of equations you can cancel or simplify all at once. This is crucial with Data Sufficiency questions, because otherwise it looks like you do not have enough information to solve the problem. You do not need to know the value for each independent piece of the equation. Your job is to simply answer the question. And that is how you think like the GMAT.
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Re: Jill has applied for a job with each of two different companies. What  [#permalink]

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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

OG 2017 New Question

Target question: What is the probability that Jill will get job offers from BOTH companies?

Given: Jill has applied for a job with each of two different companies.
Let's use the Double Matrix Method.
This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions)..

Here, we have a population of possible outcomes, and the two characteristics are:
- job offer from company A or NO job offer from company A
- job offer from company B or NO job offer from company B

ASIDE: There's no harm in naming the companies A and B

So, we can set up our matrix as follows: So, for example, the top-left box represents getting an offer from BOTH companies (I placed a star in this box to denote what the target question is asking)
The top-right box represents getting an offer from company A but NOT from company B
bottom-left box represents NOT getting an offer from company A, but getting an offer from company B
And the bottom-right box represents getting an offer from NEITHER company.

Finally, since all 4 probabilities (boxes) must add to 1, we'll add this information to the diagram... Statement 1: The probability that she will get a job offer from neither company is 0.3
Let's add this to our matrix... Does this provide enough information to determine the probability that goes in the top-left box?
NO.

Consider these two possible scenarios... In the first scenario, the probability that Jill gets job offers from BOTH companies = 0.2
In the second scenario, the probability that Jill gets job offers from BOTH companies = 0.1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The probability that she will get a job offer from exactly one of the two companies is 0.5
This one is a little trickier since there are 2 boxes that represent getting exactly 1 offer.
This top-right box represents getting exactly 1 offer, and the bottom-left box also represents getting exactly 1 offer
So, we can say that the SUM of those two boxes must be 0.5, which we'll denote as follows... Does this provide enough information to determine the probability that goes in the top-left box?
NO.

Consider these two possible scenarios... In the first scenario, the probability that Jill gets job offers from BOTH companies = 0.2
In the second scenario, the probability that Jill gets job offers from BOTH companies = 0.1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When we combine the two statements, we can see that there is only one possible value for the top-left box (since all 4 boxes must add to 1) So, the answer to the target question must be the probability that Jill gets job offers from BOTH companies = 0.2
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

NOTE: This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video:

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

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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

Intern  B
Joined: 03 Apr 2018
Posts: 38
Re: Jill has applied for a job with each of two different companies. What  [#permalink]

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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 Re: Jill has applied for a job with each of two different companies. What   [#permalink] 17 Jun 2019, 17:24

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