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DS Probability Question

This topic has 3 expert replies and 2 member replies
It'sGMATtime Newbie | Next Rank: 10 Posts Default Avatar
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DS Probability Question

Post Sat Jul 02, 2016 5:55 am
Jill has applied for a job with each of two different companies. What is the probability that she will get offers from both companies?

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

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Post Fri Dec 08, 2017 7:18 am
It'sGMATtime wrote:
Jill has applied for a job with each of two different companies. What is the probability that she will get offers from both companies?

1) The probability that she will get an offer from neither company is 0.3
2) The probability that she will get an 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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Matt@VeritasPrep GMAT Instructor
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Post Fri Jul 08, 2016 2:28 pm
Let's do it algebraically.

Suppose her probability of getting job 1 is p, and her probability of getting job 2 is q. Then we have

p(both jobs) = p * q
p(neither job) = (1 - p)*(1 - q)
p(exactly one) = p*(1 - q) + q*(1 - p)

S1:

(1 - p) * (1 - q) = .3

1 - p - q + p*q = .3

So we could have p = .7 and q = 0, or p = .5 and q = .4, or lots of other, less friendly solutions; NOT SUFFICIENT

S2:

p - qp + q - qp = .5

p + q - 2p*q = .5

Same issue as S1, also NOT SUFFICIENT

S1 + S2:

From S1, we have

pq - p - q + 1 = . 3

From S2, we have

p + q - 2pq = .5

Adding the two equations together, we have

1 - pq = .8

So pq = .2. Since pq IS the probability that Jill gets both jobs, we're set! SUFFICIENT

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800_or_bust Master | Next Rank: 500 Posts Default Avatar
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Post Sun Jul 03, 2016 10:35 am
It'sGMATtime wrote:
Jill has applied for a job with each of two different companies. What is the probability that she will get offers from both companies?

1) The probability that she will get an offer from neither company is 0.3
2) The probability that she will get an offer from exactly one of the two companies is 0.5
Probability that she will get an offer from both companies = 1 - Probability that she will get an offer from neither company - Probability that she will get an offer from exactly one of the two companies

We need both sets of information, neither alone is sufficient, so the answer is C.

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Post Sat Jul 02, 2016 9:30 am
Hi It'sGMATtime,

This question can be solved in a number of different ways (depending on how you choose to organize the information). We're asked for the probability that Jill receives job offers from BOTH of the companies that she applied to. For organizational purposes, I'm going to refer to the jobs as Job A and Job B. There are 4 possible outcomes when applying for these 2 jobs (and the total will add up to 1):

(Yes from A; No from B) + (No from A; Yes from B) + (Yes from both) + (No from both) = 1

We're trying to figure out the 3rd outcome (re: Yes from both).

1) The probability that she will get an offer from neither company is 0.3

With this Fact, we can fill in one piece of the above equation:

(Yes from A; No from B) + (No from A; Yes from B) + (Yes from both) + (.3) = 1

Unfortunately, there are still too many unknowns.
Fact 1 is INSUFFICIENT

2) The probability that she will get an offer from exactly one of the two companies is 0.5

With this Fact, while we don't know the exact value of the first TWO pieces we can still fill in the SUM of them in the above equation:

[.5] + (Yes from both) + (No from both) = 1

Unfortunately, there are still too many unknowns.
Fact 2 is INSUFFICIENT

Combined, we have the following equation:

[.5] + (Yes from both) + (.3) = 1
(Yes from both) = .2
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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Danny@GMATAcademy Junior | Next Rank: 30 Posts Default Avatar
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Post Sat Jul 02, 2016 6:07 am
Here's a video explanation for this question:

https://youtu.be/EIqnq6YprGw

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Email: GMATAcademy@outlook.com

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