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# Johnson has a corporate proposal. The probability that vice

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4471
Johnson has a corporate proposal. The probability that vice  [#permalink]

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03 Jan 2014, 18:42
1
1
00:00

Difficulty:

(N/A)

Question Stats:

63% (02:41) correct 38% (00:48) wrong based on 12 sessions

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The following information accompanies questions 4-5

Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.7. The probability that vice-president Baker will approve the proposal is 0.5. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three VPs are entirely independent of one another.

4) Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson’s proposal is funded?
(A) 0.14
(B) 0.26
(C) 0.49
(D) 0.55
(E) 0.86

5) Suppose Johnson must get the approval of at least two of the three VPs to win funding. What is the probability that Johnson’s proposal is funded?
(A) 0.14
(B) 0.26
(C) 0.49
(D) 0.55
(E) 0.86

These two problems are paired to explore a tricky question: would they have the same answer or not? Either way, what is the correct way to solve them? For a full discussion of difficult ideas in probability, as well as the complete explanations for these questions, see:

OA: (4) C, (5) D

Mike
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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
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Posts: 166
Location: United States (NY)
GMAT 1: 640 Q44 V34
GMAT 2: 710 Q48 V40
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GPA: 3.16
WE: Consulting (Venture Capital)
Re: Johnson has a corporate proposal. The probability that vice  [#permalink]

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04 Jan 2014, 22:59

4) P(A) and P(B, C , or Both)

P(A) * [P(B not C) + P(C not B)+ P(B and C)]

.7 * [(.5)(.6) + (.4)(.5) + (.5)(.4)]

=.49

5) P(2 Candidates) + P(3 Candidates)

[P(A and B not C) + P(A and C not B) + P(B and C not A)] + P(A and B and C)

[(.7)(.5)(.6) + (.7)(.4)(.5) + (.5)(.4)(.3)] + (.7)(.5)(.4)
=.55

or u can do 1 - [P(0 candidates) + P(1 candidate)]
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Re: Johnson has a corporate proposal. The probability that vice  [#permalink]

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04 Jan 2014, 23:33
mikemcgarry wrote:
The following information accompanies questions 4-5

Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.7. The probability that vice-president Baker will approve the proposal is 0.5. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three VPs are entirely independent of one another.

4) Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson’s proposal is funded?
(A) 0.14
(B) 0.26
(C) 0.49
(D) 0.55
(E) 0.86

5) Suppose Johnson must get the approval of at least two of the three VPs to win funding. What is the probability that Johnson’s proposal is funded?
(A) 0.14
(B) 0.26
(C) 0.49
(D) 0.55
(E) 0.86

These two problems are paired to explore a tricky question: would they have the same answer or not? Either way, what is the correct way to solve them? For a full discussion of difficult ideas in probability, as well as the complete explanations for these questions, see:

OA: (4) C, (5) D

Mike

1) A * B * Not C + A * Not B * C + A * B * C = 49 option c)
2) A * B * Not C + A * Not B * C + Not A * B * C + A * B * C = 55 option D)
Senior Manager
Joined: 08 Apr 2012
Posts: 323
Re: Johnson has a corporate proposal. The probability that vice  [#permalink]

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18 Sep 2014, 12:52
Hi Mike,
I'm having a little problem with the terminology.
When written " ..of at least one of the other VPs" this, for me, means that we need one more or both of them, but the answers show that you take into account just one more and deduct the option of getting both of their approvals.
Why is that?
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4471
Re: Johnson has a corporate proposal. The probability that vice  [#permalink]

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18 Sep 2014, 14:47
ronr34 wrote:
Hi Mike,
I'm having a little problem with the terminology.
When written " ..of at least one of the other VPs" this, for me, means that we need one more or both of them, but the answers show that you take into account just one more and deduct the option of getting both of their approvals.
Why is that?

Dear Ron,
With all due respect, my friend, are you sure you are reading this correctly? In the OE on the original blog page, for that problem I subtract the case of (not A and not B) --- that is, the probability of getting the approval not of both but of neither.
Does this make sense?
Mike
_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Senior Manager
Joined: 08 Apr 2012
Posts: 323
Re: Johnson has a corporate proposal. The probability that vice  [#permalink]

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21 Sep 2014, 01:34
mikemcgarry wrote:
ronr34 wrote:
Hi Mike,
I'm having a little problem with the terminology.
When written " ..of at least one of the other VPs" this, for me, means that we need one more or both of them, but the answers show that you take into account just one more and deduct the option of getting both of their approvals.
Why is that?

Dear Ron,
With all due respect, my friend, are you sure you are reading this correctly? In the OE on the original blog page, for that problem I subtract the case of (not A and not B) --- that is, the probability of getting the approval not of both but of neither.
Does this make sense?
Mike

Hi Mike,
I have read this a few time, and after your post a few more, but I still don't see it.
I'm talking about question 4, where we need A's aproval and "AT LEAST" one more.
As per your sloution: P(funding) = P(A and (B or C)) = P(A)*P(B or C)
P(B or C) = P(B) + P(C) – P(B and C)
So my question is why are we looking at just P(B or C) and subtracting P(B&C)?
Do you see what I mean here?
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4471
Re: Johnson has a corporate proposal. The probability that vice  [#permalink]

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21 Sep 2014, 13:09
1
ronr34 wrote:
mikemcgarry wrote:
ronr34 wrote:
Hi Mike,
I'm having a little problem with the terminology.
When written " ..of at least one of the other VPs" this, for me, means that we need one more or both of them, but the answers show that you take into account just one more and deduct the option of getting both of their approvals.
Why is that?

Dear Ron,
With all due respect, my friend, are you sure you are reading this correctly? In the OE on the original blog page, for that problem I subtract the case of (not A and not B) --- that is, the probability of getting the approval not of both but of neither.
Does this make sense?
Mike

Hi Mike,
I have read this a few time, and after your post a few more, but I still don't see it.
I'm talking about question 4, where we need A's aproval and "AT LEAST" one more.
As per your sloution: P(funding) = P(A and (B or C)) = P(A)*P(B or C)
P(B or C) = P(B) + P(C) – P(B and C)
So my question is why are we looking at just P(B or C) and subtracting P(B&C)?
Do you see what I mean here?

Dear Ron,
That is the OR rule, one of the most fundamental rules in probability. With all due respect, my friend, you are trying to do challenge problems and you are not clear on the fundamental rules. See this blog for a complete explanation of the OR rule:
http://magoosh.com/gmat/2012/gmat-math- ... ity-rules/
It's very important to understand all the basic rules inside-out before you start trying to wrestle with the hard stuff.
Does all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Senior Manager
Joined: 08 Apr 2012
Posts: 323
Re: Johnson has a corporate proposal. The probability that vice  [#permalink]

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21 Sep 2014, 13:52
mikemcgarry wrote:
Dear Ron,
That is the OR rule, one of the most fundamental rules in probability. With all due respect, my friend, you are trying to do challenge problems and you are not clear on the fundamental rules. See this blog for a complete explanation of the OR rule:
http://magoosh.com/gmat/2012/gmat-math- ... ity-rules/
It's very important to understand all the basic rules inside-out before you start trying to wrestle with the hard stuff.
Does all this make sense?
Mike

Right you are Mike...
This somehow slipped my mind.
I get this a lot; I know a rule but somehow forget it or overlook it when in the midst of a problem...
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Posts: 461
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Re: Johnson has a corporate proposal. The probability that vice  [#permalink]

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06 Jul 2015, 14:11
Problem 4) 7/10*(1-5/10*6/10)= 0,49 (C)
Re: Johnson has a corporate proposal. The probability that vice   [#permalink] 06 Jul 2015, 14:11
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